A25-foot ladder is leaning against the side of a house. the top of the ladder is 20 feet above the ground. to the nearest degree, find the angle of elevation between the ground and the ladder.

ANSWER:

53°

The angle of elevation between the ground and the ladder is 53°.

STEP-BY-STEP EXPLANATION:

To begin with, we will visually represent the problem as displayed in the attached diagram.

Trigonometric ratios are only applicable to right-angle triangles. The triangle in the problem is a right-angle triangle. This means we can use trigonometric ratios to solve this problem.

The values given in the problem are as follows:

Let the angle of elevation between the ground and the ladder = x

Hypotenuse of triangle = 25

Opposite side to angle = 20

This means that we will use the trigonometric ratio, sine.

sine ( theta ) = opposite side / hypotenuse

Theta = x

Opposite side = 20

Hypotenus = 25

THEREFORE:

sin ( x ) = 20 / 25

sin ( x ) = 4 / 5

x = sin^-1 ( 4 / 5 )

x = 53.13010235...

x = 53° 7' 48.37" ( in degrees )

x = 53° ( to the nearest degree )