Q:

Bob is building a wooden cabin. The cabin is 30 meters wide. He obtained a bunch of 17 meters long wooden beams for the roof of the cabin. Naturally, he 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.

Accepted Solution

A:
The roof will be in the shape of an isosceles triangle with a base length of 30 m and two sides that are 17 m. The two 17 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 15 m, and the hypotenuse will be 17. 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.

[tex]cos(\theta) = \frac{adjacent}{hypotenuse} [/tex]

[tex]cos(\theta)= \frac{15}{17}[/tex]

[tex]cos^{-1}( \frac{15}{17})=\theta [/tex]

[tex]\theta = 28.1^{\circ}[/tex]

The answer  is 28.1 degrees