Chapter 7 - Applications of Trigonometric Functions - Section 7.3 The Law of Cosines - 7.3 Assess Your Understanding - Page 559: 26

$B =90^\circ$ $A \approx53.1^\circ$ $C\approx 36.9^\circ$

1. Use the Law of Cosines, we have $B=cos^{-1}(\frac{(3)^2+(4)^2-(5)^2}{2(3)(4)})=90^\circ$ 2. Use the Law of Sines, $\frac{sinA}{4}=\frac{sin90^\circ}{5}$, thus $A=sin^{-1}(\frac{4sin90^\circ}{5})\approx53.1^\circ$ 3. We have $C\approx(180-90-53.1)=36.9^\circ$