Question

Fill in the blank. a surveyor measures the angle of elevation to a point on a mountain to be 18. the point on the mountain is horizontally 4 miles away from the surveyor. the vertical change in elevation from the point where the surveyor is standing to the point on the mountain is _____ miles. (round your answer to the nearest hundredth of a mile.)

Answer 1

Use the tangent ratio here: tan(18) = x / 4...4 tan(18) = x, and x = 1.30

Answer 2

Using tangent ratio:

`\tan \theta= \frac{\text{Opposite side}}{\text{Adjacent  side}}`

As per the statement:

a surveyor measures the angle of elevation to a point on a mountain to be 18.

⇒
`\theta = 18^(\circ)`

It is also given that the point on the mountain is horizontally 4 miles away from the surveyor.

⇒Adjacent side = 4 miles

You can see the diagram as shown below:

Using tangent ratio we have;

`\tan 18^(\circ)= \frac{\text{Opposite side}}{4}`

Multiply both sides by 4 we have;

`\text{Opposite side} = 4 \cdot \tan 18^(\circ)`

then;

`\text{Opposite side} = 4 \cdot 0.32491969623`

Simplify:

`\text{Opposite side} = 1.29967878`

Therefore, the vertical change in elevation from the point where the surveyor is standing to the point on the mountain to the nearest hundredths is 1.30 miles