SOLUTION: A scalene triangle's two angles of elevation are of sizes 28 degrees and 26 degrees. We are told that one side of the triangle is 2000m, this side lies on the ground. Can you pleas

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Question 808891: A scalene triangle's two angles of elevation are of sizes 28 degrees and 26 degrees. We are told that one side of the triangle is 2000m, this side lies on the ground. Can you please. Find the height of the triangle? This question was in a practice paper for geometric reasoning, and I couldn't figure out the answer, and I have tried to find the answer using trig, Pythagoras, and other geometric reasoning formulae. Please help me, I want to know how to do this so I can be prepared for my exam.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A scalene triangle's two angles of elevation are of sizes 28 degrees and 26 degrees.
We are told that one side of the triangle is 2000m, this side lies on the ground. Can you please. Find the height of the triangle?
:
Find the angle opposite 2000 m
180 - 28 - 26 = 126 degrees
:
Use the law of sines to find one of the other sides (b) opposite angle B, 28 degrees
b%2Fsin%2828%29 = 2000%2Fsin%28126%29
.809b = .469 * 2000
b = 939%2F.809
b = 1160.6
:
This is the hypotenuse of a right triangle formed by the height which is opposite the 26 degree angle
therefore
Sin(26) = h%2F1160.6
h = 1160.6 * .438
h = 509 meters is the height
:
did this make sense to you?