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riadik2000 [5.3K]
3 years ago
12

A surveyor wants to know the length of a tunnel built through a mountain. According to his equipment, he is

Mathematics
1 answer:
MrMuchimi3 years ago
5 0

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

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