Question

A house is 5.8 m wide. The roof is being designed by an architect so that one side will be longer in order to accommodate solar panels. If the angle at the rooftop is to be 110°, and the angle of elevation of the shorter side is to be 45°, find the lengths of the rafters needed to support each side of the roof.

Answer 1

To find the lengths of the rafters needed to support each side of the roof, use the sine ratio with the given angles and the width of the house. The shorter side can be found using the angle of elevation, and the longer side can be found using the angle at the rooftop.

Step-by-step explanation:

To find the lengths of the rafters needed to support each side of the roof, we can use trigonometric ratios. Let's start by finding the length of the shorter side of the roof. We have the angle of elevation as 45° and the width of the house as 5.8m. Using the sine ratio, we can set up the equation:

sin(45°) = opposite/hypotenuse

Solving for the opposite side (the shorter side of the roof), we get: opposite = sin(45°) * hypotenuse

Now, let's find the length of the longer side of the roof. We have the angle at the rooftop as 110° and the width of the house as 5.8m. Again, using the sine ratio, we can set up the equation:

sin(110°) = opposite/hypotenuse

Solving for the opposite side (the longer side of the roof), we get: opposite = sin(110°) * hypotenuse