TE6 Checkit

source/precalculus/exercises/bank.xml

@@ -436,15 +436,14 @@
                Use the law of sines and/or the law of cosines to solve non-right triangles.
             </description>
         </outcome>
-<!--
         <outcome>
             <title>Applications of Trigonometry</title>
             <slug>TE6</slug>
             <path>outcomes/TE/TE6</path>
             <description>
                Solve applications that require the use of trigonometry to find a side or angle.
             </description>
-        </outcome> -->
+        </outcome> 
 
     </outcomes>
 </bank>

source/precalculus/exercises/outcomes/TE/TE6/generator.sage

@@ -0,0 +1,213 @@
+load("../../../source/common/sagemath/library.sage")
+class Generator(BaseGenerator):
+    def data(self):
+
+        names=["Mateo", "Nina", "Ophelia", "Pierre", "Quinn", "Rosa", "Serena", "Thad", "Ursula","Victor"]
+
+        scenario1=choice(["ladder","elevation","angleofclimb","fire","scuba"])
+        #Ladder against a building
+        if scenario1=="ladder":
+            ladder_length=choice([12,16,..,48])
+            #Keep it 60-80 degrees ish
+            height = choice([int(sin(pi/3)*ladder_length),..,int(sin(80/180*pi)*ladder_length)])
+            angle = round(arcsin(height/ladder_length)*180/pi,1)
+            variables1 = { "height": height,
+                           "ladder": ladder_length,
+                           "angle": angle
+                         }
+        #Angle of elevation/depression
+        elif scenario1=="elevation":
+            scenario=choice(["scenarioA","scenarioB"])
+            units=choice(["ft","m"])
+            if units=="ft":
+                height=choice([500,600,..,4000])
+            else:
+                height=choice([100,150,..,1000])
+            angle = choice([10..35])
+            distance=round(height/sin(angle*pi/180),0)
+            variables1={ scenario: {
+                          "name": choice(names),
+                          "units": units,
+                          "height": height,
+                          "angle": angle,
+                          "distance": distance,
+                          }
+                       }
+        #Airplane climbing
+        elif scenario1=="angleofclimb":
+            angle = choice([12..20])
+            height= choice([5000,6000,..,20000])
+            distance=round(height/tan(angle*pi/180),0)
+            variables1={  "height": height,
+                          "angle": angle,
+                          "distance": distance,
+                          "distance_miles": round(distance/5280,0),
+                       }
+        elif scenario1=="fire":
+            angles=sample([40..70],2)
+            angles.sort()
+            angle3 = 180-angles[0]-angles[1]
+            distance=choice([10..40])
+            d=round(sin(angles[0]*pi/180)/sin(angle3*pi/180)*distance,1)
+
+            rangers=sample(["Arata", "Botha", "Chang", "Dinh", "Emerson", "Fabian", "Hernandez", "Ishikawa", 
+                            "Jones", "Khoury", "Lee", "Martinez", "Naser", "Okpara", "Rodriguez", 
+                            "Shalhoub", "Thomas", "Williams", "Zhang"],2)
+            ranger_answer=rangers[1]
+            if choice([True,False]):
+                angles.reverse()
+                rangers.reverse()
+
+            directions=["left","right"]
+            shuffle(directions)
+
+            variables1 = {
+                            "park": choice(["Yosemite National Park", "the Sierra National Forest", 
+                                            "Sequoia National Park", "Kings Canyon National Park",
+                                            "the Stanislaus National Forest", "the Tahoe National Forest",
+                                            "Pinnacles National Park", "the Inyo National Forest",
+                                            "the Sequoia National Forest"]),
+                            "distance": distance,
+                            "angle1": angles[0],
+                            "angle2": angles[1],
+                            "ranger1": rangers[0],
+                            "ranger2": rangers[1],
+                            "direction1": directions[0],
+                            "direction2": directions[1],
+                            "answer": d,
+                            "ranger_answer": ranger_answer,
+                         }
+        elif scenario1=="scuba":
+            angles=sample([40..70],2)
+            #angles.sort()
+            angle3 = 180-angles[0]-angles[1]
+            distance=choice([10..40])
+            d1=round(sin(angles[1]*pi/180)/sin(angle3*pi/180)*distance,1)
+            d2=round(sin(angles[0]*pi/180)/sin(angle3*pi/180)*distance,1)
+
+            names=sample([
+                        "Astera", "Alexi",
+                        "Boudica", "Byron",
+                        "Claudette", "Carlos",
+                        "Devonta", "Deborah",
+                        "Evie", "Envita",
+                        "Federico", "Frankie",
+                        "Greny", "Greta",
+                        "Hani", "Harlin",
+                        "Inigo", "Imogene",
+                        "Jun Young", "Jarvis",
+                        "Khalil", "Kiara",
+                        "Lisandro","Leslie",
+                        "Marcelo", "Melissa",
+                        "Nicolas", "Nicole",
+                        "Pedro", "Pham",
+                        "Raquel", "Rodrigo" ],2)
+
+            variables1 = {
+                            "depth": choice([5..25]),
+                            "animal": choice(["leopard shark", "green moray", "manta ray", "sea turtle"]),
+                            "distance": distance,
+                            "angle1": angles[0],
+                            "angle2": angles[1],
+                            "name1": names[0],
+                            "name2": names[1],
+                            "distance1": d1,
+                            "distance2": d2,
+                         } 
+
+
+
+
+
+        scenario2=choice(["airport","hiker","boats","ceiling","carpentersquare","bridge"])
+        #SAS, Law of cosines
+        if scenario2=="airport":
+            plane1,plane2=sample([" Boeing 737", " Boeing 747", " Boeing 767", "n Airbus A320", "n Airbus A330", 
+                                  " McDonnel Douglas MD11", " Bombardier CRJ200", "n Embraer E170"],2)
+            d1,d2=sample([10..75],2)
+            heading1,heading2=sample([10,20,..,350],2)
+            distance=round(sqrt(d1^2+d2^2-2*d1*d2*cos(abs(heading1-heading2)*pi/180)),1)
+            variables2={ "plane1": plane1,
+                        "plane2": plane2,
+                        "distance1": d1,
+                        "distance2": d2,
+                        "heading1": heading1,
+                        "heading2": heading2,
+                        "distance3": distance,
+                        "units": choice(["miles","kilometers"])
+                      }
+        elif scenario2=="hiker":
+            d1,d2=sample([2..10],2)
+            angle=choice([20,25,..,80]+[100,105..,140])
+            distance=round(sqrt(d1^2+d2^2-2*d1*d2*cos(pi-angle*pi/180)),1)
+            variables2={ "distance1": d1,
+                        "distance2": d2,
+                        "angle": angle,
+                        "direction": choice(["left","right"]),
+                        "distance3": distance,
+                        "units": choice(["miles","kilometers"])
+                      }
+        ##AAS Law of sines
+        elif scenario2=="boats":
+            angle1,angle2=sample([5,10,..,75],2)
+            d1=choice([10..50])
+            d2=round(d1*sin(angle2*pi/180)/sin(angle1*pi/180),1)
+            d3=round(d1*sin((180-angle1-angle2)*pi/180)/sin(angle1*pi/180),1)
+            variables2={ "angle1": angle1,
+                         "angle2": angle2,
+                         "distance1": d1,
+                         "distance2": d2,
+                         "distance3": d3,
+                         "specifier": choice(["taller", "newer", "red"]),
+                         "units": choice(["nautical miles", "miles", "kilometers"])
+                       }
+        elif scenario2=="ceiling":
+            angle=choice([85,..,89]+[91..95])
+            d=round(choice([2,2.25,..,5]),2)
+            units=choice(["inches","centimeters"])
+            if units=="centimeters":
+                d=2*d
+            e=round(d*sin(angle*pi/180)/sin((pi-angle*pi/180)/2),2)
+            variables2={ "angle": angle,
+                         "distance1": d,
+                         "distance2": e,
+                         "units": units,
+                       }
+        #SSS
+        elif scenario2=="carpentersquare":
+            angle=choice([85,..,89]+[91..95])
+            d1,d2=sample([4,4.5,..,20],2)
+            d3=round(sqrt(d1^2+d2^2-2*d1*d2*cos(angle*pi/180)),1)
+            angle=round(arccos((d3^2-d1^2-d2^2)/(-2*d1*d2))*180/pi,1)
+            units=choice(["inches","centimeters"])
+            if units=="centimeters":
+                d1,d2,d3=(2*d1,2*d2,2*d3)
+            variables2={ "angle": angle,
+                         "distance1": round(d1,1),
+                         "distance2": round(d2,1),
+                         "distance3": d3,
+                         "units": units,
+                       }
+        elif scenario2=="bridge":
+            d=sample([50..100],3)
+            angle_choice = choice(["smallest","largest"])
+            if angle_choice=="smallest":
+                d.sort()
+            else:
+                d.sort(reverse=True)
+
+            angle=round(arccos((d[0]^2-d[1]^2-d[2]^2)/(-2*d[1]*d[2]))*180/pi,1)
+            shuffle(d)
+            variables2={ 
+                        "d1": d[0],
+                        "d2": d[1],
+                        "d3": d[2],
+                        "angle_choice": angle_choice,
+                        "angle": angle,
+                        "units": choice(["feet", "meters"])
+                       }
+
+
+        tasks=[ {scenario1: {**variables1}}, {scenario2: {**variables2}}]
+        shuffle(tasks)
+        return { "tasks": tasks }

source/precalculus/exercises/outcomes/TE/TE6/template.xml

@@ -0,0 +1,148 @@
+<knowl mode="exercise" xmlns="https://spatext.clontz.org" version="0.2">
+  <!--{{#tasks}}-->
+  <knowl>
+    <!-- First task options -->
+      <!--{{#ladder}}-->
+        <content>
+          <p>A <m>{{ladder}}\ \text{ft}</m> ladder is leaned against a wall that is
+            <m>{{height}}\ \text{ft}</m> tall.  What angle does the ladder make with the ground?</p>
+        </content>
+        <outtro>
+          <p><m>{{angle}}^\circ</m></p>
+        </outtro>
+      <!--{{/ladder}}-->
+      <!--{{#elevation}}-->
+        <!--{{#scenarioA}}-->
+        <content>
+          <p>{{name}} is standing on top of a cliff <m>{{height}}</m> {{units}} above a lake.
+             They see a boat on the lake, and measure an angle of depression from the horizon
+             to the boat of <m>{{angle}}^\circ</m>.  How far away from {{name}} is the boat?
+          </p>
+        </content>
+        <outtro>
+          <p><m>{{distance}}</m> {{units}}</p>
+        </outtro>
+        <!--{{/scenarioA}}-->
+        <!--{{#scenarioB}}-->
+        <content>
+          <p>{{name}} sees a person on top of a <m>{{height}}</m> {{units}} tall cliff.
+             They measure an angle of elevation from the ground to the person of <m>{{angle}}^\circ</m>.  
+             How far away from {{name}} is the other person?
+          </p>
+        </content>
+        <outtro>
+          <p><m>{{distance}}</m> {{units}}</p>
+        </outtro>
+        <!--{{/scenarioB}}-->
+      <!--{{/elevation}}-->
+      <!--{{#angleofclimb}}-->
+        <content>
+          <p>An airplane takes off from a runway and climbs at angle of <m>{{angle}}^\circ</m>. 
+            How far along the ground does the plane need to travel to reach an altitude of 
+            <m>{{height}}\ \text{ft}</m>? 
+          </p>
+        </content>
+        <outtro>
+          <p><m>{{distance}}\ \text{ft}</m>, or about <m>{{distance_miles}}</m> miles</p>
+        </outtro>
+      <!--{{/angleofclimb}}-->
+      <!--{{#fire}}-->
+        <content>
+          <p>In {{park}}, two fire towers are located <m>{{distance}}</m> miles apart.  Ranger {{ranger1}}
+             is in one tower, and measures that the fire is <m>{{angle1}}^\circ</m> to the {{direction1}} of
+             the other tower.  Ranger {{ranger2}} is in the other tower, and measures that the fire is 
+             <m>{{angle2}}^\circ</m> to the {{direction2}} of the first tower.  Which ranger is closer to the 
+             fire, and how far away are they from the fire? 
+          </p>
+        </content>
+        <outtro>
+          <p>Ranger {{ranger_answer}} is <m>{{answer}}</m> miles from the fire. </p>
+        </outtro>
+      <!--{{/fire}}-->
+      <!--{{#scuba}}-->
+        <content>
+          <p>{{name1}} and {{name2}} are scuba diving and are <m>{{depth}}</m> meters below the surface of the water,
+            and are horizontally <m>{{distance}}</m> meters apart.
+            They spot a {{animal}} swimming below them.  The angle of depression from {{name1}} to the {{animal}} is 
+            <m>{{angle1}}^\circ</m> and the angle of depression from {{name2}} to the {{animal}} is <m>{{angle2}}^\circ</m>.
+            How far is each diver from the {{animal}}?
+          </p>
+        </content>
+        <outtro>
+          <p>{{name1}} is <m>{{distance1}}</m> meters away and {{name2}} is <m>{{distance2}}</m> meters away. </p>
+        </outtro>
+      <!--{{/scuba}}-->
+    <!-- Second task options -->
+      <!--{{#airport}}-->
+        <content>
+          <p>A{{plane1}} is heading directly away from an airport on a heading of <m>{{heading1}}^\circ</m>,
+            and is <m>{{distance1}}</m> {{units}} away from the airport.
+            The pilot hears over the radio that there is a{{plane2}} flying at a heading of <m>{{heading2}}^\circ</m> 
+            that is currently <m>{{distance2}}</m> {{units}} from the airport.
+            How far apart are the two planes?
+          </p>
+        </content>
+        <outtro>
+          <p><m>{{distance3}}</m> {{units}}</p>
+        </outtro>
+      <!--{{/airport}}-->
+      <!--{{#ceiling}}-->
+        <content>
+          <p>In a particular room, the ceiling meets the wall at a <m>{{angle}}^\circ</m>angle.  A trim carpenter wants 
+            to fit a piece of crown moulding that meets the ceiling and the wall both <m>{{distance1}}</m> {{units}} from the corner.
+            How wide should this piece of crown moulding be?
+          </p>
+        </content>
+        <outtro>
+          <p><m>{{distance2}}</m> {{units}}</p>
+        </outtro>
+      <!--{{/ceiling}}-->
+      <!--{{#hiker}}-->
+        <content>
+          <p>A hiker walks in a straight line for <m>{{distance1}}</m> {{units}}.  They turn <m>{{angle}}^\circ</m>
+            to their {{direction}} and walk another <m>{{distance2}}</m> {{units}}.  If they then want to walk
+            in a straight line back to their starting place, how far must they walk?
+          </p>
+        </content>
+        <outtro>
+          <p><m>{{distance3}}</m> {{units}}</p>
+        </outtro>
+      <!--{{/hiker}}-->
+      <!--{{#boats}}-->
+        <content>
+          <p>A boat is lost, but sees two lighthouses on the shore.  The boat measures an angle of <m>{{angle1}}^\circ</m>
+            between the two lighthouses, and fortunately establishes radio contact with a person in the {{specifier}} lighthouse.
+            They report that the lighthouses are <m>{{distance1}}</m> {{units}} apart, and they see an angle of 
+            <m>{{angle2}}^\circ</m> between the boat and the other lighthouse.  How far is the boat from each lighthouse?
+          </p>
+        </content>
+        <outtro>
+          <p><m>{{distance3}}</m> {{units}} from the {{specifier}} lighthouse, and <m>{{distance2}}</m> {{units}} from the other lighthouse.</p>
+        </outtro>
+      <!--{{/boats}}-->
+      <!--{{#carpentersquare}}-->
+        <content>
+          <p>A carpenter is trying to determine if two pieces of wood meet at a right angle, and does not have a square.
+             One piece of wood is <m>{{distance1}}</m> {{units}} long, and the other is <m>{{distance2}}</m> {{units}} long.
+             She measures the distance between the other ends of the pieces of wood as <m>{{distance3}}</m> {{units}}.
+             What angle do the two pieces of wood make with each other?
+          </p>
+        </content>
+        <outtro>
+          <p><m>{{angle}}^\circ</m></p>
+        </outtro>
+      <!--{{/carpentersquare}}-->
+      <!--{{#bridge}}-->
+        <content>
+          <p>A bridge is supported by triangular braces. If the sides of each brace have lengths 
+            <m>{{d1}}</m> {{units}}, <m>{{d2}}</m> {{units}}, and <m>{{d3}}</m> {{units}}, find the 
+            measure of the {{angle_choice}} angle created by the sides of the brace.
+          </p>
+        </content>
+        <outtro>
+          <p><m>{{angle}}^\circ</m></p>
+        </outtro>
+      <!--{{/bridge}}-->
+  </knowl>
+  <!--{{/tasks}}-->
+</knowl>