Chapter 13 - Section 13.2 - Using Trigonometric Ratios to Find Angles - Exercise - Page 546: 16

$$A=35.5°$$ $$B=54.5°$$

Find angle A. We can use the trigonometric function for tangent to find angle A. $tan A=\frac{a}{b}$ $tan A=\frac{351.6m}{493.0m}$ $tan A=0.7132$ Now we solve for A by multiplying both sides of the equation by the inverse tangent. So, $tan^{-1}(tan A) = tan^{-1}(0.7132)$ $A = tan^{-1}(0.7132)$ $A=35.5°$ 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 $B=90°-A$ $B=90°-35.5°$ $B=54.5°$