Question

A ladder has an angle of elevation of 32 ∘ If the ladder is 18 ft long, how high up the building does the ladder reach? Round to the nearest tenth.

Answer 1

To find the height reached by an 18 ft ladder at a 32° angle of elevation, we use the sine function and determine that the ladder reaches approximately 9.5 ft up the building.

Step-by-step explanation:

To determine the height up the building that an 18 ft ladder reaches at a 32° angle of elevation, we can use trigonometric ratios, specifically the sine function. The angle of elevation is the angle between the ground and the ladder, and the ladder itself acts as the hypotenuse in a right-angled triangle. By using the sine function, which is the ratio of the opposite side (height reached by the ladder) over the hypotenuse (length of the ladder), we can find the height.The sine of 32° (θ) is equal to the height reached (h) divided by the ladder length (l), or sin(θ) = h/l. Using the 18 ft ladder length, we set up the following equation: sin(32°) = h/18 ft. Solving for the height, we get h = 18 ft ⋅ sin(32°).
Calculating this, we find the height reached by the ladder:
h ≈ 18 ft ⋅ 0.5299; h ≈ 9.5382 ft
Rounding to the nearest tenth gives us a height of approximately 9.5 ft.