Question

A surveyor wants to know the length of a tunnel built through a mountain. According to his equipment, he is
located 54
meters from one entrance of the tunnel, at an angle of 56
to the perpendicular. Also according to his equipment, he is 31

meters from the other entrance of the tunnel, at an angle of 13
to the perpendicular. Based on these measurements, find the length of the entire tunnel.
Do not round any intermediate computations. Round your answer to the nearest tenth.

Answer 1

Answer:

Length of the tunnel is 51.7 meters

Step-by-step explanation:

We are given that,

The surveyor is located 54 meters from one entrance at an angle of 56°.

The surveyor is located 31 meters from one entrance at an angle of 13°.

Let the length of the tunnel = x meters

So, using the law of cosines, we get,

$x^2=54^2+31^2-2\times 54\times 31\times \cos 69$

i.e. $x^2=2916+961-3348\times 0.3584$

i.e. $x^2=3877-1199.9$

i.e. $x^2=2677.1$

i.e. x = 51.7 meters

Hence, the length of the tunnel is 51.7 meters