Question

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

Answer 1

The answer is 1.3 (This is rounded to the nearest hundredth.)

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 degree.

Angle of elevation
`(\theta)` = 18 degree.

It is also given that:

the point on the mountain is horizontally 4 miles away from the surveyor.

Let y be the vertical change in elevation from the point where the surveyor is standing to the point on the mountain.

See the diagram as shown below in the attachment

we have;

Opposite side = y miles and adjacent side = 4 miles

Using tangent ratio:

`\tan 18^(\circ) = (y)/(4)`

then;

`0.3249196 = (y)/(4)`

Multiply both sides by 4 we have;

`1.2996 = y`

or

`y \approx 1.3` miles.

Therefore, 1.3 miles is the the vertical change in elevation from the point where the surveyor is standing to the point on the mountain