Q:

Will mark Brainliest and 50 points.Suppose that a roof is built so that the angle at the peak and the lengths of the sides, which differ, are known. How would the width of the house be determined?

Accepted Solution

A:
Answer:In that scenario, you will have the shape of a triangle, with the measures of two sides (the two slopes of the roof) and one angle (the peak angle).Based on that it's easy to find out the length of the other side of the triangle, which in this case would the width of the house, going from the ending tip of the left part of the roof to the ending tip of the right part of the roof.Let's name a and c the sides of the roof, and the angle B the peak of the roof.We are then looking for the length of the b side, that would connect sides a and c.By the Cosines Law, we know that[tex]cos(B) = \frac{c2 + a2 - b2}{2ca}[/tex]Which we can transform to isolate b, this way:[tex]b = \sqrt{a^{2} + c^{2} - 2 * a * c * cos(B)}[/tex]So, you just have to enter the length of both sides of the roof and the angle, to get the measurement of the width of the house.