Posted by **huss** on Tuesday, September 17, 2013 at 4:51am.

a tree is x meter high the angle of elevation of its top from a point p on the ground is 23 degree . from another point q 10 meter from p and in line with p and foot of the tree , the angle of elevation is 32 degree. find x

- math -
**Reiny**, Tuesday, September 17, 2013 at 8:10am
make a sketch, label the top of the tree A, and its bottom as B

label the point with the 23° angle P and the point with the 32°angle Q

We can find all the angles in triange PQA

angle P = 23, angle PQA = 148 , then angle PAQ = 9°

by sine law:

AQ/sin23 = (p-q)/sin9

AQ = (p-q)sin23/sin9

in the right-angled triangle, assuming the tree is vertical

sin 32 = x/AQ

x = AQ sin32

x = ((p-q)sin23/sin9) sin32

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