Question

TREES From point A,

the angle of elevation to the top of a pine tree is 42°.
From point B,
on the same side of the tree, the angle of elevation to the top of the tree is 50°.


If point A
and point B
are located 12
feet apart and are both at ground level, what is the approximate height of the tree to the nearest foot?

feet

Answer 1

44 ft

Explanation:

You want to know the height of a tree whose top is at angles of elevation of 42° and 50° from points 12 feet apart.

Tangent

The tangent of an angle is related to the side lengths of a right triangle by ...

Tan = Opposite/Adjacent

This tells us the length of the side adjacent to the angle of elevation is ...

Adjacent = Opposite/Tan

Application

Here, the height of the tree is the side of the triangle opposite the angle of elevation, and the difference of adjacent sides is 12 ft:

12 = h/tan(42°) -h/tan(50°)

h = 12/(1/tan(42°) -1/tan(50°)) ≈ 12/(1.11061 -0.83910) ≈ 44.197

The approximate height of the tree is 44 feet.