Question

The entrance to a horizontal mining tunnel has collapsed, trapping the miners inside.

The rescue team decide to drill a vertical escape shaft from a position 200 m further
up the hill. If the hill slopes at 23◦ from the horizontal, how deep does the rescue shaft
need to be to meet the horizontal tunnel? Answer to one decimal place.

Answer 1

Answer: 78.1 meters

Step-by-step explanation

The diagram is shown below.

We have a right triangle with an unknown vertical leg (which I'll call x) and a known hypotenuse that is 200 meters long.

We use the sine ratio to connect the opposite and hypotenuse.

sin(angle) = opposite/hypotenuse

sin(23) = x/200

x = 200*sin(23)

x = 78.1462256978548 approximately

x = 78.1

Make sure your calculator is in degree mode.