TE6 Checkit

[siwelwerd]

This could use a few more scenarios still. Maybe @tdegeorge has some ideas?

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[tdegeorge]

@siwelwerd Am I doing this problem wrong? I am not getting the same answer...

[siwelwerd]

@siwelwerd Am I doing this problem wrong? I am not getting the same answer...

Should be $\dfrac{8000}{\tan(19^\circ)}$, right? My phone calculator says that's 23234.

[tdegeorge]

@siwelwerd Am I doing this problem wrong? I am not getting the same answer...

Should be 8000 tan ⁡ ( 19 ∘ ) , right? My phone calculator says that's 23234.

Oh sorry - I copied the wrong question! I meant this one:

[tdegeorge]

@siwelwerd Am I doing this problem wrong? I am not getting the same answer...

Should be 8000 tan ⁡ ( 19 ∘ ) , right? My phone calculator says that's 23234.

Oh sorry - I copied the wrong question! I meant this one:

Is this law of cosines?

[siwelwerd]

Ohhhh I think I programmed it as $\sqrt{5^2+7^2-2\cdot5\cdot7\cdot\cos(115^\circ)}\approx 10.2$, but should be $\sqrt{5^2+7^2-2\cdot5\cdot7\cdot\cos((180-115)^\circ)}\approx 6.7$?

[tdegeorge]

@siwelwerd Don't know how great these examples are, but how about some of these or something like them?

1. A bridge is supported by triangular braces. If the sides of each brace have lengths 52 feet, 64 feet, and 70 feet, find the measure of the smallest angle created by the sides of the brace.

2. Fire towers A and B are located 10 miles apart. Rangers at fire tower A spot a fire at 42°, and rangers at fire tower B spot the same fire at 64°. How far from tower A is the fire to the nearest tenth of a mile?

3. Two scuba divers are 20 m apart below the surface of the water. They both spot a shark that is below them. The angle of depression from diver 1 to the shark is 47 degrees and the angle of depression from diver 2 to the shark is 40 degrees. How far is each diver from the shark?

4. To estimate the length of a lake, Caleb starts at one end of the lake and walks 95 m. He then turns and walks on a new path, which is 120 degrees fo the direction he was first walking and walks 87 m more until he arrives at the other end of the lake. Approximately how long is the lake?

[tdegeorge]

Ohhhh I think I programmed it as 5 2 + 7 2 − 2 ⋅ 5 ⋅ 7 ⋅ cos ⁡ ( 115 ∘ ) ≈ 10.2 , but should be 5 2 + 7 2 − 2 ⋅ 5 ⋅ 7 ⋅ cos ⁡ ( ( 180 − 115 ) ∘ ) ≈ 6.7 ?

Yep - that's what I did!

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[siwelwerd]

@siwelwerd Don't know how great these examples are, but how about some of these or something like them?

1. A bridge is supported by triangular braces. If the sides of each brace have lengths 52 feet, 64 feet, and 70 feet, find the measure of the smallest angle created by the sides of the brace.
2. Fire towers A and B are located 10 miles apart. Rangers at fire tower A spot a fire at 42°, and rangers at fire tower B spot the same fire at 64°. How far from tower A is the fire to the nearest tenth of a mile?
3. Two scuba divers are 20 m apart below the surface of the water. They both spot a shark that is below them. The angle of depression from diver 1 to the shark is 47 degrees and the angle of depression from diver 2 to the shark is 40 degrees. How far is each diver from the shark?
4. To estimate the length of a lake, Caleb starts at one end of the lake and walks 95 m. He then turns and walks on a new path, which is 120 degrees fo the direction he was first walking and walks 87 m more until he arrives at the other end of the lake. Approximately how long is the lake?

I think the fourth one is essentially that hiker one. I like the other 3 so I'll try to add those later this morning.

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[siwelwerd]

@tdegeorge Added those three scenarios, would appreciate your double checking them though!

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[tdegeorge]

@tdegeorge Added those three scenarios, would appreciate your double checking them though!

For the fire example, I am not getting the same answer. For example, for this problem, I am getting that Ranger Naser is closer and the distance is 10.89 miles from the fire (using the law of sines):

[tdegeorge]

@siwelwerd I also get different answers for the scuba diving questions

[siwelwerd]

For the fire example, I am not getting the same answer. For example, for this problem, I am getting that Ranger Naser is closer and the distance is 10.89 miles from the fire (using the law of sines):

I had a bug in the calculation of the number, but since Naser measures a smaller angle, the side opposite of Naser is the smallest leg of the triangle. However, the side opposite of Naser is the distance from the fire to Khoury, so it is Ranger Khoury who is 10.9 miles away.

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[tdegeorge]

For the fire example, I am not getting the same answer. For example, for this problem, I am getting that Ranger Naser is closer and the distance is 10.89 miles from the fire (using the law of sines):

I had a bug in the calculation of the number, but since Naser measures a smaller angle, the side opposite of Naser is the smallest leg of the triangle. However, the side opposite of Naser is the distance from the fire to Khoury, so it is Ranger Khoury who is 10.9 miles away.

Oh, I guess I am reading it wrong. I interpreted it as Khoury was in one tower and he measured the angle for the other tower to be 67 degrees (the tower that Naser is in).

[tdegeorge]

@siwelwerd I also get different answers for the scuba diving questions

I'm still getting a different answer for the scuba diving questions...

[siwelwerd]

Drat, I thought I fixed it yeserday. Can you share your solution to one of them? Just want to make sure I'm not doing something silly.

[tdegeorge]

• https://6957c9dd.tbil.pages.dev/preview/precalculus/exercises/TE6/

Oh wait - it's me! I forgot to subtract from 180 for the third angle (smh)