etch and Solve each problem given below. Round your answers to two decimal places. 1.) The angle of elevation from point \( A \) to the top of a hill is \( 49^{\circ} \). If point \( A \) is 400 feet from the base of the hill, how high is the hill? 2.) Find the angle of elevation of the sun when a 12.5 -meter-tall telephone pole casts a 18 -meter- long shadow.

1.) We are given the angle of elevation \( \theta = 49^{\circ} \) and the horizontal distance \( d = 400 \) feet. For a right triangle, the tangent of the angle is the ratio of the opposite side (hill height \( h \)) to the adjacent side (distance \( d \)). Thus, we have \[ \tan(49^{\circ}) = \frac{h}{400}. \] Solving for \( h \): \[ h = 400 \cdot \tan(49^{\circ}). \] Using a calculator for \( \tan(49^{\circ}) \): \[ \tan(49^{\circ}) \approx 1.15. \] Thus, \[ h \approx 400 \cdot 1.15 \approx 460.16 \text{ feet}. \] 2.) We are given the telephone pole height \( H = 12.5 \) meters and the length of the shadow \( s = 18 \) meters. The angle of elevation \( \theta \) is given by the relationship: \[ \tan(\theta) = \frac{H}{s} = \frac{12.5}{18}. \] Calculating the quotient: \[ \frac{12.5}{18} \approx 0.69. \] To find the angle \( \theta \), take the inverse tangent: \[ \theta = \arctan(0.69). \] Using a calculator: \[ \theta \approx 34.99^{\circ}. \] Thus, the angle of elevation of the sun is approximately \( 34.99^{\circ} \).