Question

A ladder leans against the wall and reaches a

point 24 feet up the wall. The base of the ladder
is 6 feet from the wall.
What is the measure of the angle that the ladder makes with the wall? Explain

Answer 1

The measure of the angle that the ladder makes with the wall is 48.59°.

Step-by-step explanation:

The measure of the angle that the ladder makes with the wall can be found using trigonometry.

Given that the ladder reaches a point 24 feet up the wall and the base of the ladder is 6 feet from the wall, we can use the sine function to find the angle.

Sine is defined as the ratio of the opposite side to the hypotenuse.

So in this case, sin(angle) = opposite/hypotenuse = 24/25.

Therefore, the measure of the angle is sin^(-1)(24/25) = 48.59°.

Answer 2

The base would represent the side adjacent to the angle and the height up the wall would be the opposite side. Using the tangent^-1 (opposite over adjacent) function we are looking for the tan^-1 of 6/24 or 14.04°