Triangle Applications Help?

[frosthawk97]

Hello! Back again needing some more test correction help, but this time I only have 3 problems I need help with.

Problem 1:

Anna and Elsa are 164 feet apart and see a kite flying in the air between them. The angle of elevation from Anna to the kite is 33 degrees and the angle of elevation from Elsa to the kite is 47 degrees. How far is the kite from Elsa?

So far, I've drawn a picture that looks like this:

Two things I'm wondering:
1) Have I drawn the correct type of triangle?
2) If I am correct, is it possible for me to divide the triangle into two right triangles that have a side of 82 feet?

Other than that, this problem's got me stumped. I know I can't exactly use Law of Sines or Cosines, and I'm drawing a blank as to how I can figure out any other sides/angles to get the distance.

Problem 2:
Given ▲ABC with ∠C = 56°, a = 15, & c = 9, what is the measure of angle ∠A?

Since I was given a triangle with an angle and two sides, I know this is a type of ambiguous case, however I wasn't too sure if it was a case of two triangles or not. The main thing that is sticking out to me in particular is that side C is smaller than side A, doesn't that mean there's no triangle since side C is supposed to be the biggest side? If there is a way to solve this, then an explanation would be heavily appreciated. ^_^"

Problem 3:
Given ▲ABC, ∠A = 43°, c = 14, and a = 15, find the measure of ∠B?

The only thing I've worked up so far is to find ∠C by using Law of Sines, and then I just did 180 - (∠A + ∠C) to find ∠B, but I have the odd feeling that is not correct, and that this triangle could possibly be a 2 triangle case?

Thanks in advanced, again~

 

[stapel]

Problem 1: Anna and Elsa are 164 feet apart and see a kite flying in the air between them. The angle of elevation from Anna to the kite is 33 degrees and the angle of elevation from Elsa to the kite is 47 degrees. How far is the kite from Elsa?

So far, I've drawn a picture that looks like this:

Two things I'm wondering:
1) Have I drawn the correct type of triangle?

It looks fine to me.

2) If I am correct, is it possible for me to divide the triangle into two right triangles that have a side of 82 feet?

How are you getting this? (Since the angles of elevation are different, obviously the kite is not exactly midway between them, so you can't be getting "82" from "(1/2)*164". So how?)

I would continue on by drawing the other indicated bits. The kite is some distance above the ground; draw the vertical line and label this as "h" for "height". This height line splits the horizontal distance between the two viewers into two (unequal) portions. Since you're needing to find the distance to Elsa, I'd label her portion of the line as "e"; then the rest of the line is "164 - e".

This information allows you to create two right triangles, each with known angles, and for which you have expressions for the height ("opposite") and the bases ("adjacent"). I think I'd try something with tangents....

Problem 2: Given Triangle ABC with m(Angle C) = 56°, length of side a = 15, and length of side c = 9, what is the measure of angle A?

Since I was given a triangle with an angle and two sides, I know this is a type of ambiguous case, however I wasn't too sure if it was a case of two triangles or not.

You figure this out by working the exercise. Either there will be two valid solutions, or there won't be. See what you get!

Problem 3: Given Triangle ABC, m(angle A) = 43°, length of side c = 14, and length of side a = 15, find the measure of Angle B.

Isn't this the exact same set-up as Problem 2 (being "Angle, Side, Side", or "***")...?

 

[Deleted member 4993]

Hello! Back again needing some more test correction help, but this time I only have 3 problems I need help with.

Problem 1:

Anna and Elsa are 164 feet apart and see a kite flying in the air between them. The angle of elevation from Anna to the kite is 33 degrees and the angle of elevation from Elsa to the kite is 47 degrees. How far is the kite from Elsa?

So far, I've drawn a picture that looks like this:

Two things I'm wondering:
1) Have I drawn the correct type of triangle?
2) If I am correct, is it possible for me to divide the triangle into two right triangles that have a side of 82 feet?

Other than that, this problem's got me stumped. I know I can't exactly use Law of Sines or Cosines, and I'm drawing a blank as to how I can figure out any other sides/angles to get the distance.

Problem 2:
Given ▲ABC with ∠C = 56°, a = 15, & c = 9, what is the measure of angle ∠A?

Since I was given a triangle with an angle and two sides, I know this is a type of ambiguous case, however I wasn't too sure if it was a case of two triangles or not. The main thing that is sticking out to me in particular is that side C is smaller than side A, doesn't that mean there's no triangle since side C is supposed to be the biggest side? If there is a way to solve this, then an explanation would be heavily appreciated. ^_^"

Problem 3:
Given ▲ABC, ∠A = 43°, c = 14, and a = 15, find the measure of ∠B?

The only thing I've worked up so far is to find ∠C by using Law of Sines, and then I just did 180 - (∠A + ∠C) to find ∠B, but I have the odd feeling that is not correct, and that this triangle could possibly be a 2 triangle case?

Thanks in advanced, again~

.

Problem 1

Apply law of sines in a triangle.