Chapter 13 - Section 13.2 - Using Trigonometric Ratios to Find Angles - Exercise - Page 546: 15

$$A=41.9°$$ $$B=48.1°$$

Find angle A. We can use the trigonometric function for tangent to find angle A. $tan A=\frac{a}{b}$ $tan A=\frac{243.2km}{271.5km}$ $tan A=0.8958$ Now we solve for A by multiplying both sides of the equation by the inverse tangent. So, $tan^{-1}(tan A) = tan^{-1}(0.8958)$ $A = tan^{-1}(0.8958)$ $A=41.9°$ 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 $B=90°-A$ $B=90°-41.9°$ $B=48.1°$