A25-ft ladder is leaning against a building. if the base of the ladder is 8 ft from the base of the building, what is the angle of elevation of the ladder? (round your answer to one decimal place.)

Step-by-step explanation:

This is not a difficult problem of trigonometry. The first step is to draw a sketch of the situation in order to make the reasoning simpler (see the attached figure).

The segment OB represents the side of the building, while the segment CA represents the ladder and CO the distance of the ladder to the base of the building. We want to find the measure of the angle ∠ACO. Notice that OAC is a right triangle. From the statement of the problem we know that CA = 25 ft and CO = 8 ft.

Using the formula for the cosine of an angle:

cos∠ACO = CO/AC = 8/25= 0.32.

Now, we must use the inverse cosine function in order to find the measure of the angle (in degrees). An approximate value is

arccos(0.32) = 71.33707512°,

and rounding to one decimal place we have that the measure of the angle ∠ACO = 71.3°.

If we want to give the measure in radians, we get

arccos(0.32) = 1.24506684,

and rounding to one decimal place

∠ACO = 1.2 radians.

24 units

step-by-step explanation: