Question

The angle of elevation to a nearby tree from a point on the ground is

measured to be 54°. How tall is the tree if the point on the ground is 52
feet from the tree? Round your answer to the nearest hundredth of a
foot if necessary.

Answer 1

71.57 feet

Explanation:

Helps to draw a figure

See attached figure to support explanation

AB represents the tree. Let the height of the tree be h feet

AC represents the length of the person from the base of the tree. This length is 52 feet

Angle ACB is the angle of elevation and given as 52°

The tangent of the angle ACB = Side opposite/Side Adjacent = AB/AC

Plugging in values that we have,

tan(54°) = h/52

or

h/52 = tan(54°)

h = 52 x tan(54°)

h = 71.5718 feet

Rounding this to the nearest hundredth of a foot gives
Height of the tree = 71.57 feet