A fireman leans a 40-ft long ladder up against a building. The base of the ladder creates an angle of elevation of 32 degrees with the ground. How far is the base of the ladder from the base of the building? Round to the nearest whole foot, if necessary.
if the distance is x,
x/40 = cos 32°
evaluate that and solve for x
To find the distance between the base of the ladder and the base of the building, we can use trigonometry. In this case, we have the length of the ladder (40 ft) and the angle of elevation (32 degrees).
We can use the sine function, which relates the angles of a right triangle to the ratio of the opposite side to the hypotenuse. In this case, the opposite side is the distance between the base of the ladder and the base of the building, and the hypotenuse is the length of the ladder.
sin(angle) = opposite/hypotenuse
Plugging in the values, we get:
sin(32 degrees) = opposite/40 ft
Now, we can solve for the opposite side (the distance we're looking for). Rearranging the equation, we have:
opposite = sin(32 degrees) * 40 ft
Using a scientific calculator or trigonometric table, we can find that sin(32 degrees) is approximately 0.5299. Multiplying this value by 40 ft, we get:
opposite = 0.5299 * 40 ft ≈ 21.20 ft
Therefore, the distance between the base of the ladder and the base of the building is approximately 21.20 feet. Rounded to the nearest whole foot, it would be 21 feet.