Question

A surveyor wants to know the length of a tunnel built through a mountain. According to his equipment, he is located 120 meters from one entrance of the tunnel, at an angle of 42° to the perpendicular. Also according to his equipment, he is 101 meters from the other entrance of the tunnel, at an angle of 28⁰ 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. 120 meters 42° 28° 101 meters​

Answer 1

The length of the entire tunnel is 127.88 meters by using cosine law or formulae.

Here we can use the formulae of cosine when two sides a and b and angle between then is given we can apply it.

$c^{2} =a^{2} +b^{2} -2ab cos (\alpha )$

Let us take surveyor as point A

one end of the tunnel denoted by point B

other end of the tunnel denoted by point C.

The length of AB is 101 meters

length of AC is 120 meters.

Measure of angle at point A = 42° + 28° =70°

Now lets find the length of tunnel

=$\sqrt{(120^{2})+(101^{2})-2.(120)(101) cos (70) }$

=$\sqrt{14400+10201-24240(0.34)}$

=$\sqrt{24601-8246}$

$\sqrt{16355}$

=127.88 meters.

Hence the length of the entire tunnel is 127.88 meters.

You can find more about cosine law: brainly.com/question/28135764

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