Use the markings in the image to answer the following questions (drawing not to scale): a. as you look at sides a, b, c, and d, which side lengths are possible to calculate based on the information in the image? b. for those side lengths which are possible to calculate, what steps would you take to calculate each side? c. for those side lengths we don’t have enough information to calculate, what information would you need to complete the calculations?

First of all, we have to observe this triangles separated by the height. These small and big triangles are similar according to the Angle-Angle-Angle principle.

a. We can find all of these length using the cosine of the angle, Pythagoras theorem and the principle of the similarity of triangles.

b. According to the cosine of the angle we can write that, cosθ = 12/a = 5/13 and from here a = 31.2. After finding that using Pythagoras theorem, we can write that . According to the similarity of the triangles, we can write that 31.2/d = 28.8/12 and d = 13. Applying Pythagoras theorem we find that c = 5.

c. We already gave the answer for this question in part b