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

2. The gable end width at the base is roughly 6.74 meters, and the rafters have an approximate 47.8° angle.

3. There are about 820.91 meters separating the lighthouse's base from the ship.

Finding the rafters' angle (θ):

θ=
`arcsin (7.5/10.2)`

Now, by means of a calculator:

θ≈
`arcsin(0.735 )`≈ 47.8°

Next, determine the gable end's width at the base (w):

w=l⋅
`cos` (θ)

w≈10.2⋅
`cos`(47.8°) ≈ 6.74m

So, The gable end width at the base is roughly 6.74 meters, and the rafters have an approximate 47.8° angle.

3. Lighthouse and Ship:

To find the distance from the base of the lighthouse to the ship (d):

d=h/tan(α)

Now, by means of a calculator:

d≈ 55/tan(3.8°)≈ 820.91m

Therefore, There are about 820.91 meters separating the lighthouse's base from the ship.