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Question $1$ of $5$ $\newline$ You are skiing on a mountain with an altitude of $1200$ meters. The angle of depression is $21^{\circ}$ . You are trying to find the distance you will be sking down the mountain. Which trigonometric function will you use to solve this? $\newline$ Select the correct response. $\newline$ $\cos$ $\newline$ $\sin$ $\newline$ $\tan$

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Add and subtract integers: word problems

Full solution

Q. Question

1

of

5

\newline

You are skiing on a mountain with an altitude of

1200

meters. The angle of depression is

21^{\circ}

. You are trying to find the distance you will be sking down the mountain. Which trigonometric function will you use to solve this?

\newline

Select the correct response.

\newline

\cos

\newline

\sin

\newline

\tan

Relate Altitude and Angle: To solve for the distance down the mountain, we need to relate the altitude of the mountain to the angle of depression and the distance we are trying to find. The angle of depression from the top of the mountain to the bottom is congruent to the angle of elevation from the bottom to the top due to alternate interior angles being equal when two lines are parallel and one is a transversal. Therefore, the angle of elevation is also $21$ degrees. We are given the altitude (opposite side) and need to find the hypotenuse (the distance skiing down the mountain). The trigonometric function that relates the opposite side to the hypotenuse is the sine function.
Angle of Depression: We will use the sine function, which is defined as $\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$ . In this case, $\theta$ is the angle of elevation, which is $21$ degrees, the opposite side is the altitude of the mountain ( $1200$ meters), and the hypotenuse is the distance down the mountain we are trying to find.

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