Question

What do the ratios of the side lengths for a right triangle depend on? In particular, do they depend on the lengths of the sides? What about the angle measurements of the right triangle? Use your observations from the previous exercises to explain.

Answer 1

Answer and Step-by-step explanation:

The ratios can be used to find the measures of acute angles in a right triangle when you know the measures of the two sides of the triangle. You must determine which ratio to use depending on which sides are given. Then, use the inverse trigonometric functions on your calculator to find the angle.

Answer 2

The ratios of the sides of a right triangle do not change if you change the lengths of the sides while keeping the angles fixed. But if you change the measure of the acute angle A, then the ratios change. The ratios depend only on the measure of the acute angle A. All right triangles with a congruent acute angle have the same ratios because the triangles are similar.