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.
[tex]c^{2} =a^{2} +b^{2} -2ab cos (\alpha )[/tex]
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
=[tex]\sqrt{(120^{2})+(101^{2})-2.(120)(101) cos (70) }[/tex]
=[tex]\sqrt{14400+10201-24240(0.34)}[/tex]
=[tex]\sqrt{24601-8246}[/tex]
[tex]\sqrt{16355}[/tex]
=127.88 meters.
Hence the length of the entire tunnel is 127.88 meters.
You can find more about cosine law: https://brainly.com/question/28135764
#SPJ9
