Answer:
Using tangent ratio:
[tex]\tan \theta = \frac{\text{opposite side}}{\text{Adjacent side}}[/tex]
As per the statement:
A surveyor measures the angle of elevation to a point on a mountain to be 18 degree.
Angle of elevation [tex](\theta)[/tex] = 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:
[tex]\tan 18^{\circ} = \frac{y}{4}[/tex]
then;
[tex]0.3249196 = \frac{y}{4}[/tex]
Multiply both sides by 4 we have;
[tex]1.2996 = y[/tex]
or
[tex]y \approx 1.3[/tex] 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
