Chapter 13 - Section 13.2 - Using Trigonometric Ratios to Find Angles - Exercise - Page 546: 6

$$A=48.1°$$ $$B=41.9°$$

Find angle A. We can use the trigonometric function for tangent to find angle A. $cos A=\frac{b}{c}$ $cos A=\frac{409km}{612cm}$ $cos A=0.6683$ Now we solve for A by multiplying both sides of the equation by the inverse cosine. So, $cos^{-1}(cos A) = cos^{-1}(0.6683)$ $A = cos^{-1}(0.6683)$ $A=48.1°$ 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 $B=90°-A$ $B=90°-48.1°$ $B=41.9°$