Chapter 13 - Section 13.2 - Using Trigonometric Ratios to Find Angles - Exercise - Page 546: 3

$$A=24.4°$$ $$B=65.6°$$

Find angle A. We can use the trigonometric function for tangent to find angle A. $cos A=\frac{b}{c}$ $cos A=\frac{39.7cm}{43.6cm}$ $cos A=0.9106$ Now we solve for A by multiplying both sides of the equation by the inverse cosine. So, $cos^{-1}(cos A) = cos^{-1}(0.9106)$ $A = cos^{-1}(0.9106)$ $A=24.4°$ 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 $B=90°-A$ $B=90°-24.4°$ $B=65.6°$