Chapter 13 - Section 13.2 - Using Trigonometric Ratios to Find Angles - Exercise - Page 546: 22

$$A=46.7°$$ $$B=43.3°$$

Find angle A. We can use the trigonometric function for cosine to find angle A. $cos A=\frac{b}{c}$ $cos A=\frac{2450km}{3570km}$ $cos A=0.6863$ Now we solve for A by multiplying both sides of the equation by the inverse cosine. So, $cos^{-1}(cos A) = cos^{-1}(0.6863)$ $A = cos^{-1}(0.6863)$ $A=46.7°$ 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 $B=90°-A$ $B=90°-46.7°$ $B=43.3°$