Question

Barbara is building a wooden cabin. The cabin is 424242 meters wide. She obtained a bunch of 272727 meters long wooden beams for the roof of the cabin. Naturally, she wants to place the roof beams in such an angle that each pair of opposite beams would meet exactly in the middle. What is the angle of elevation, in degrees, of the roof beams? Round your final answer to the nearest tenth.

Answer 1

The roof will be in the shape of an isosceles triangle with a base length of 42 m and two sides that are 27 m. The two 27 m beams will have the same angle of elevation since they have to might in the middle.

So to find the angle of elevation, we can split the roof in half vertically to create a right triangle. The base will now be 21 m, and the hypotenuse will be 27 . Now we can use a trigonometry function to solve for the angle. We know the hypotenuse and the side adjacent to the angle, so we can use cosine.

$cos(\theta) = \frac{adjacent}{hypotenuse}$

$cos(\theta)= \frac{21}{27}$

$cos^{-1}( \frac{21}{27})=\theta$

$\theta = 38.9^{\circ}$

The answer is 38.9 degrees