Question

A surveyor walks 100 m up a hill whichslopes at an angle of 24° to the hori-zontal. Calculate, correct to the near-est metre, the height through which herises.

Answer 1

Explanation

From the statement, we know that a surveyor walks a distance h = 100 m over a hill with a slope of degree θ = 24°. We must compute the height that the surveyor goes up.

Using this data, we make the following diagram:

From the diagram, we see a right triangle with:

• angle θ = 24°,

,

• opposite side OS = height,

,

• hypotenuse H = 100 m.

From trigonometry, we know the following relation:

$\sin\theta=\frac{OS}{H}.$

Replacing the data from above, we have:

$OS=H\cdot\sin\theta=100m\cdot\sin(24\degree)\cong36.81m\cong37m.$

So the surveyor rises to a height of 37 m.

Answer

The surveyor rises to a height of 37 m.