# math

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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 -

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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