Question

8.) John wants to measure the height of a tree. He walks

exactly 100 feet from the base of the tree and looks up. The
angle from the ground to the top of the tree is 33º . How tall is
the tree?

Answer 1

here you have to use the law of sines

let tree make an angle of 83 deg.with the ground. (YZ)angle ZYX = 83deg

he walks 100 feet away from tree to point X (YX)angle YXZ= 33 deg

so remaining angle YZX = 64 deg

triangle YXZ is formed

sin A /a = sin B /b = sin C /c

Sin YZX/100 = sin YXZ/ YZ

sin 64/100 = sin 33/YZ

100 * sin 33/sin 64 = YZ

100*0.54/0.898= YZ

YZ= 60.13 feet the height of the tree

Explanation: