Trigonometry-16
From Homeworkwiki
A tree is broken by the wind. The top struck the ground at an angle of 300 at a distance of
30 m from the root. Find the whole height of the tree.
Solution: Let B be the point where the tree is broken.
The whole height of the tree is AB + BT
AB / AT = tan 300
AB = AT x 1/√3 = 30 x 1/√3 m
BT = √ (AT2 + AB2)
= √302 + (30/√3)2 = √(900 + 300) = √1200 = 20 √3
AB + BT = 30/√3 + 20 √3 = 10√3 + 20√3 = 30√3
Hence, the whole height of the tree = 30√ m
