Question

You are standing 40 meters from the base of a tree that leans 8o away from you. The angle of elevation from you to the top of the tree is 20o. Find the slant height of the tree.

Answer 1

the height of the tree is 15.49 m

Explanation:

Step 1:

From the figure, we can determine ∠ATB by using the fact that the sum of all the angles in a triangle add up to 180°:

∠ ATB = 180° - 98° - 20°

∠ ATB = 62°

Step 2:

Therefore, using the law of sines, we can determine the height of the tree.

TB / sin(20°) = 40 / sin(62°)

TB = 40 × (sin(20°) / sin(62°))

TB = 15.49 m

Therefore, the height of the tree is 15.49 m