Question

A surveyor wants to know the length of a tunnel built through a mountain. According to her equipment, she is located 340 meters from one entrance of the tunnel, at an angle of 58° to the perpendicular. Also according to her equipment, she is 193 meters from the other entrance of the tunnel, at an angle of 21° to the perpendicular. Based on these measurements, find the length of the entire tunnel.

Answer 1

The length of the entire tunnel is 357.5 m

Using trigonometric concept :

• sine = opposite / Hypotenus

Sin(58) = d / 340

d = 340 × sin(58)

d = 288.33 meters

For the other side ;

Sin(21) = d / 193

d = 193 × sin(21)

d = 69.16 meters

The length of tunnel:

• 69.16 + 288.33 = 357.49

The length of the entire tunnel is 357.5 m