1. **State the problem:** We need to find the angles $m\angle B$, $m\angle A$, $m\angle W$, and $m\angle H$ given their sine, cosine, or tangent values. 2. **Formula used:** To find an angle from its trigonometric ratio, use the inverse trig functions: - $m\angle = \sin^{-1}(\text{value})$ for sine - $m\angle = \cos^{-1}(\text{value})$ for cosine - $m\angle = \tan^{-1}(\text{value})$ for tangent 3. **Calculate each angle:** - For $\sin B = 0.4848$: $$m\angle B = \sin^{-1}(0.4848)$$ Using a calculator, $$m\angle B \approx 28.95^\circ$$ Rounded to nearest degree: $$m\angle B = 29^\circ$$ - For $\cos A = 0.7431$: $$m\angle A = \cos^{-1}(0.7431)$$ Using a calculator, $$m\angle A \approx 42.12^\circ$$ Rounded to nearest degree: $$m\angle A = 42^\circ$$ - For $\tan W = 19.0811$: $$m\angle W = \tan^{-1}(19.0811)$$ Using a calculator, $$m\angle W \approx 86.99^\circ$$ Rounded to nearest degree: $$m\angle W = 87^\circ$$ - For $\cos H = 0.6157$: $$m\angle H = \cos^{-1}(0.6157)$$ Using a calculator, $$m\angle H \approx 52.01^\circ$$ Rounded to nearest degree: $$m\angle H = 52^\circ$$ 4. **Summary:** - $m\angle B = 29^\circ$ - $m\angle A = 42^\circ$ - $m\angle W = 87^\circ$ - $m\angle H = 52^\circ$