[Math] What are the unknown lengths are angles for the roof

algebra-precalculustrianglestrigonometric seriestrigonometry

enter image description here

Sharma is building a shed and wants to determine the measurements for the roof. The span of
the roof will be 10 feet and she plans to use a 5:12 roof pitch. This means that the roof will rise 5 inches for every 12 horizontal inches. Complete her diagram by determining the unknown angle measures, to the nearest degree, and side lengths, to the nearest tenth of a foot.

I understand SOH-CAH-TOA, but I am having trouble understanding how to answer this question. Any guidance in solving this would be greatly appreciated, thank you!

Best Answer

Hints:

  • $2e = 10$
  • $\frac{d}{e} = \frac{5}{12}$
  • $d^2 + e^2 = c^2$
  • $\tan a = \frac{d}{e}$
  • $a + b = 90^\circ$
Related Question