1. **Determine angle C in the triangle with sides 5 and 13** Given: $ \cos \Phi = \frac{a}{h} = \frac{5}{13} $ We use the cosine inverse function to find angle C: $$ \Phi = \cos^{-1} \left( \frac{5}{13} \right) $$ Calculate: $$ \Phi \approx \cos^{-1} (0.3846) \approx 67.38^\circ $$ Rounded to the nearest degree: $$ \boxed{67^\circ} $$ 2. **Find the height of the flagpole given shadow length and angle of elevation** Given: - Shadow length (adjacent side) = 7.9 m - Angle of elevation = 59° Using the tangent function (TOA): $$ \tan(59^\circ) = \frac{\text{opposite}}{\text{adjacent}} = \frac{h}{7.9} $$ Solve for height $ h $: $$ h = 7.9 \times \tan(59^\circ) $$ Calculate: $$ h \approx 7.9 \times 1.6643 = 13.15 \text{ m} $$ Rounded to the nearest tenth: $$ \boxed{13.2 \text{ m}} $$