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11.1.3 Quiz: Introduction to Trigonometry
Question 5 of 10
2 Points
Fill in the blank.
A surveyor measures the angle of elevation to a point on a mountain to be 12
• The point on the mountain is horizontally 5 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 here

Respuesta :

Answer:

Vertical change in the elevation is 1.06 miles.

Step-by-step explanation:

Distance between the surveyor C and the point A on a mountain = 5 miles

Angle of elevation of the point A from surveyor = 12°

We have to calculate the vertical height AB of the point A from the surveyor.

tan C = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]

tan 12° = [tex]\frac{AB}{BC}[/tex]

tan 12° = [tex]\frac{h}{5}[/tex]

h = 5tan12°

h = 1.063 miles

h ≈ 1.06 miles

Therefore, vertical change in the elevation is 1.06 miles.

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