Question

A surveyor wants to know the length of a tunnel built through a mountain according to his equipment he is located 340 m from the entrance of the tunnel at an angle of 58° to the perpendicular also according to his equipment he is 193 m from the other entrance of the tunnel other angle of 21° to the perpendicular based on these measurements find the length of the entire tunnel

Answer 1

Length of the tunnel is 357.50 meters

Explanation:

We are given that,

The surveyor is located 340 meters from one entrance at an angle of 58°.

The surveyor is located 193 meters from one entrance at an angle of 21°.

Let the length of the tunnel = x meters

Using the Law of Cosines,

`x^(2) =(340)^(2)+(193)^(2)-(2)(340)(193)cos(21+58)\\x^(2) =115600+37249-131240cos(79)\\x^(2) =115600+37249-25041.77255\\x^(2) =127807.2274\\x=√(127807.2274) \\x=357.50 meters\\`

Hence, the length of the tunnel is 357.50 meters