Question

Suppose that you are headed toward a plateau 37.9 meters high. If the angle of elevation to the top of the plateau is ​38.5 degrees, how far are you from the base of the​ plateau?

Answer 1

47.65 meters

Explanation:

We can form a right triangle to model this situation (see the attached image), whose side
`d` we are trying to solve for, as it models "your" distance from the base of the plateau.

To solve for
`d`, we can use the trigonometric ratio tangent, since we are given one angle of a right triangle and the length of the opposite leg, and we are trying to solve for the adjacent leg.

`\tan(x)=\frac{\text{opposite}}{\text{adjacent}}`

↓ plugging in the given values

`\tan(38.5\textdegree) = \frac{37.9 \text{ m}}{d}`

↓ taking the reciprocal of both sides

`(1)/(\tan(38.5\textdegree)) = \frac{d}{37.9 \text{ m}}`

↓ multiplying both sides by 37.9 m

`(37.9)/(\tan(38.5\textdegree)) \text{ m} = d`

We can now approximate
`d` by plugging the left side of the equation into a calculator.

`d \approx 47.65 \text{ m}`

So, "you" are approximately 47.65 meters from the base of the plateau.