Chapter 13 - Section 13.2 - Using Trigonometric Ratios to Find Angles - Exercise - Page 546: 8

$$A=30°$$ $$B=60°$$

Find angle A. We can use the trigonometric function for tangent to find angle A. $tan A=\frac{a}{b}$ $tan A=\frac{36.2mm}{62.7mm}$ $tan A=0.5774$ Now we solve for A by multiplying both sides of the equation by the inverse tangent. So, $tan^{-1}(tan A) = tan^{-1}(0.5774)$ $A = tan^{-1}(0.5774)$ $A=30°$ Find angle B. We know that in right triangles the sum of the acute angles is 90°. So, $A+B=90°$ Solving for $B$, we get $B=90°-A$ $B=90°-30°$ $B=60°$