Question

2. If the height of a gable end of a roof is 7.5 m and the rafters are 10.2 long, at

what angle do the rafters slope, and how wide is the gable end at the base?
3. From the top of a lighthouse 55 m above the water the angle of depression of a
ship is 3.8°. Find the distance from the base of the lighthouse to the ship.

Answer 1

The angle of the rafters' slope is approximately 47.8°, and the width of the gable end at the base is approximately 6.62 m.

Step-by-step explanation:

To find the angle at which the rafters slope, we can use the properties of a right triangle. The height of the gable end is the opposite side, and the length of the rafters is the hypotenuse. By using the sine function, we can find the angle:

sin(angle) = height / length

sin(angle) = 7.5 m / 10.2 m

angle = arcsin(0.735)

angle ≈ 47.8°

To find the width of the gable end at the base, we can use the properties of a right triangle again. The height is the opposite side, and the width is the adjacent side. By using the cosine function, we can find the width:

cos(angle) = width / length

cos(47.8°) = width / 10.2 m

width = cos(47.8°) * 10.2 m

width ≈ 6.62 m