1. Problem: Write the trigonometric ratios for the given triangles. **a. tan A in triangle ABC** (right angle at C, sides 28 cm, 24 cm, 10 cm) - tan A = opposite/adjacent = BC/AC = 24/10 **b. cos B in triangle BCD** (right angle at C, sides BC = 4.6 cm, BD = 8.7 cm) - cos B = adjacent/hypotenuse = BC/BD = 4.6/8.7 **c. sin B in triangle BCD** - sin B = opposite/hypotenuse = CD/BD - CD = \sqrt{BD^2 - BC^2} = \sqrt{8.7^2 - 4.6^2} = \sqrt{75.69 - 21.16} = \sqrt{54.53} \approx 7.38 - sin B = 7.38/8.7 2. Problem: Find the measure of each indicated angle to the nearest degree. **a. ∠F in triangle GFH** (right angle at G, GF = 10, GH = 13) - Use cosine: cos F = adjacent/hypotenuse = GF/GH = 10/13 - ∠F = cos^{-1}(10/13) \approx 39.12^\circ \approx 39^\circ **b. ∠B in triangle BCD** (right angle at C, BC = 4.6, BD = 8.7) - cos B = BC/BD = 4.6/8.7 - ∠B = cos^{-1}(4.6/8.7) \approx 57.5^\circ \approx 58^\circ **c. ∠U in triangle STU** (right angle at T, ST = 10.8, SU = 18.0) - cos U = ST/SU = 10.8/18.0 - ∠U = cos^{-1}(10.8/18.0) \approx 54.46^\circ \approx 54^\circ **d. ∠E in triangle CDE** (right angle at D, CD = 5, DE = 9) - cos E = CD/DE = 5/9 - ∠E = cos^{-1}(5/9) \approx 56.25^\circ \approx 56^\circ --- **Summary of formulas used:** - tan \theta = opposite/adjacent - cos \theta = adjacent/hypotenuse - sin \theta = opposite/hypotenuse - Pythagorean theorem: hypotenuse^2 = adjacent^2 + opposite^2 - Inverse cosine to find angles: \theta = cos^{-1}(ratio) All angles rounded to nearest degree.