Question

question
as shown in the diagram below, you are skiing on a mountain with an altitude of 1200 feet. the angle of depression is 21°. find the distance x you ski down the mountain to the nearest foot.

Explanation:

Step1: Identify the trigonometric ratio

Since we know the opposite side (altitude = 1200 ft) and need to find the hypotenuse ($x$), we use the sine ratio. $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 21^{\circ}$, opposite = 1200. So, $\sin(21^{\circ})=\frac{1200}{x}$.

Step2: Solve for $x$

Rearrange the equation to $x=\frac{1200}{\sin(21^{\circ})}$. We know that $\sin(21^{\circ})\approx0.3584$. Then $x=\frac{1200}{0.3584}$.

Step3: Calculate the value of $x$

$x=\frac{1200}{0.3584}\approx3348$

Answer:

$3348$