Note: the image below is a temporary reference image. If the author of this problem wants to finish the problem, the triangle below can be replaced with the correct reference image.

*An engineer is planning to make an roof with a $\displaystyle 30$ m frame base. The angle of the slope of the roof to the base is $\displaystyle \theta$. The sloped sides are congruent. Use the information to answer items (a)-(b).*

*(a) Find the area of the roof.*
*(b) If the area of each square tile is $\displaystyle 1{\text{ m}}^{2}$, find the number of tiles and right triangle tiles necessary to fully cover the roof.*

*The idea of this worked example is to measure the area of a roof, as seen in plan, and then divide by $\displaystyle \cos \theta$, where $\displaystyle \theta$ is the angle of slope of the roof, to get the area of tiles needed. And then the quantity of tiles. Intention is to use a real roof's plan, where all the slopes are the same.*