Question

1. while standing on top of a hill at a ski resort, lisa spots the ski lodge below. if the vertical height of the hill is 1209 feet and the angle of depression is 53°, what distance must lisa ski in order to reach the lodge?

Explanation:

Step1: Use sine function

The vertical height \( h = 1209\) feet is the side opposite to the angle of \(53^{\circ}\). Let the distance Lisa needs to ski be \(x\) (the hypotenuse of the right - triangle). The sine function is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(53^{\circ})=\frac{1209}{x}\).

Step2: Solve for \(x\)

We know that \(\sin(53^{\circ})\approx0.7986\). Then, from \(\sin(53^{\circ})=\frac{1209}{x}\), we can rewrite it as \(x=\frac{1209}{\sin(53^{\circ})}\). Substitute \(\sin(53^{\circ}) = 0.7986\) into the formula: \(x=\frac{1209}{0.7986}\).

Answer:

\(x = 1514\) feet (rounded to the nearest whole number)