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.
⇒[tex]\theta = 18^{\circ}[/tex]
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;
[tex]\tan 18^{\circ}= \frac{\text{Opposite side}}{4}[/tex]
Multiply both sides by 4 we have;
[tex]\text{Opposite side} = 4 \cdot \tan 18^{\circ}[/tex]
then;
[tex]\text{Opposite side} = 4 \cdot 0.32491969623[/tex]
Simplify:
[tex]\text{Opposite side} = 1.29967878[/tex]
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
