Chapter 13 - Section 13.2 - Using Trigonometric Ratios to Find Angles - Exercise - Page 546: 23

$$A=64.6°$$ $$B=25.4°$$

Find angle A. We can use the trigonometric function for sine to find angle A. $sin A=\frac{a}{c}$ $sin A=\frac{8897m}{9845m}$ $sin A=0.9037$ Now we solve for A by multiplying both sides of the equation by the inverse sine. So, $sin^{-1}(sin A) = sin^{-1}(0.9037)$ $A = sin^{-1}(0.9037)$ $A=64.6°$ 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 $B=90°-A$ $B=90°-64.6°$ $B=25.4°$