A surveyor wants to know the length of a tunnel built through a mountain. Accord

Question

A surveyor wants to know the length of a tunnel built through a mountain. According to his equipment, he is located 243 meters from one entrance of the tunnel, at an angle of 47° to the perpendicular. Also according to his equipment, he is 186 meters from the other entrance of the tunnel, at an angle of 27° 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. Note that the figure below is not drawn to scale. 7027 186 meters 243 meters

Explanation / Answer

angle opposite to the length of the tunnel is

47 + 27 = 74 degrees

let length of tunnel is d meters

applying law of cosines

d = sqrt ( 243^2 + 186^2 - 2 (243)(186) cos 74)

d = 262.2

length of tunnel = 262.2 meters

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