What does this mean? How do I do this?

Question

595. To the nearest tenth of a degree, find the sizes of the acute angles in the 5-12-13 triangle and in the 9-12-15 triangle. This enables you to calculate the sizes of the angles in the 13- 14-15 triangle. Show how to do it, then invent another example of this sort.

Answer 1

5² + 12² = 13²

So, the triangle is a right triangle

Let θ be the angle opposite the side of length 12

sinθ = 12/13 So, θ = Sin^-1(12/13) and the angle opposite the side of length 5 is 90° - θ.