Chapter 13 - Section 13.2 - Using Trigonometric Ratios to Find Angles - Exercise - Page 546: 4

$$A=13.8°$$ $$B=76.2°$$

Find angle A. We can use the trigonometric function for tangent to find angle A. $tan A=\frac{a}{b}$ $tan A=\frac{171km}{695km}$ $tan A=0.2460$ Now we solve for A by multiplying both sides of the equation by the inverse tangent. So, $tan^{-1}(tan A) = tan^{-1}(0.2460)$ $A = tan^{-1}(0.2460)$ $A=13.8°$ 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 $B=90°-A$ $B=90°-13.8°$ $B=76.2°$