Question

A 25-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 1

To find the angle of elevation between the ground and the ladder, we can use the tangent function and the given measurements. The angle is approximately 39.8 degrees.

Step-by-step explanation:

To find the angle of elevation between the ground and the ladder, we can use trigonometry. Since the top of the ladder is 20 feet above the ground and the ladder is 25 feet long, we can use the opposite and adjacent sides of a right triangle. The trigonometric function that relates these sides is the tangent function:

tan(angle) = opposite/adjacent

Plugging in the known values, we get: tan(angle) = 20/25

Using a calculator to find the inverse tangent (arctan) of both sides, we get the angle to be approximately 39.8 degrees to the nearest degree.

Answer 2

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 )