Barbara is building a wooden cabin. The cabin is 42 meters wide. She obtained a bunch of 27 meters long wooden beams for the roo
f 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?
Answer: The angle of elevation should be 38.9 degrees.
To find this answer, it is always best to draw a picture of the building. The point of the roof, will be directly over the middle of the cabin. Therefore, we could draw an altitude down from the top to the cabin and create a right triangle.
This would form a triangle with an adjacent side and hypotenuse with our needed angle.
We could write and solve the following cosine equation:
Vertical angles form when we have an X shape like this. They are opposite one another and always congruent. Angles 2 and 4 is the other set of vertical angles.
