Chapter 13 - Section 13.2 - Using Trigonometric Ratios to Find Angles - Exercise - Page 546: 10

$$A=63.4°$$ $$B=26.6°$$

Find angle A. We can use the trigonometric function for cosine to find angle A. $cos A=\frac{b}{c}$ $cos A=\frac{21.34m}{47.65m}$ $cos A=0.4478$ Now we solve for A by multiplying both sides of the equation by the inverse cosine. So, $cos^{-1}(cos A) = cos^{-1}(0.4478)$ $A = cos^{-1}(0.4478)$ $A=63.4°$ 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 $B=90°-A$ $B=90°-63.4°$ $B=26.6°$