Question

A surveyor wishes to find the height of a mountain. He selects points A and B on level ground along the same line of sight to the mountain. He measures the distance AB to be 1503 m and the angles of elevation of the top of the mountain from the points to be 16.9° from A and 22.3° from B.

a) Calculate the distance to the top of the mountain from point B.

The triangle that A and B and their angles of elevation makes, I called triangle ABC; I calculated C's angle to be 180°-16.9°-22.3°=140.8°... I feel like this is where I went wrong, is it incorrect to do this? I probably visualised it incorrectly again or something..

Anyway, my solution, using sine law:

b/sin22.3° = 1503/140.8°
b = 1503sin22.3°/140.8°
b = 4

The answer should be 6060m. So I'm clearly doing something completely wrong here.

Answer 1

Sorry, a) should say, "calculate the distance to the top of the mountain from point A," not point B.

Answer 2

if the angle of elevation at B is 22.3° then angle B in your triangle ABC is its supplement: 157.7°.

b = 1503 sin157.7° / sin5.4° = 6060

Answer 3

But in the triangle I was thinking of/the one I drew, the mountain is inside triangle ABC...? I don't really understand why I would have to take the supplementary angle of 22.3; I'm not disagreeing with you, I can see that you're right, I just don't understand how and I want to understand for future reference.

Answer 4

Hmmm. What is C? I used C for the top of the mountain. What other point is of interest?

Answer 5

Dnt knw