Question

Trigonometry came in handy this past summer for farmer karl. To cut two facial boards for the roof of his chicken coop, he needed to find the length L and the angles α and β. given the diagram below, help karl verify his calculations.

Answer 1

@ranga

Answer 2

We will have to assume the roof is symmetrical and therefore the right edge of the triangle is also of length L. This will be an isosceles triangle and the angle on the right side will also be alpha. The Draw button is not working and so I can't illustrate this properly with a diagram. But tan(alpha) = opposite / adjacent = 18 / 24 (I got 24 by dividing 48 by 2).
tan(alpha) = 18/24 = 3/4
alpha = arctan(3/4) = 36.9 degrees.

Three angles of a triangle add up to 180 degrees. alpha + alpha + beta = 180 degrees.
beta = 180 - (2 * alpha) = 180 - (2 * 36.9) = 106.2 degrees.

Answer 3

thank you for the explanation

Answer 4

you are welcome.