Answered By Leonardo F

It's a classic trigonometric problem. We need to construct a figure like the one shown below.

The value of angle alpha is 48.9 degrees. Hence, the value of the angle A will be 180 - alpha = 180-48.9=131.1 degrees.

The value of angle gamma is 26.7 degrees. Hence, since the sum of the internal angles of a triangle is always 180 degrees, we have the value of angle B:

B=180-131.1-26.7=22.2 degrees.

We can apply now the sine law to discover the value of y (or the distance between the second person caught in the avalanche and the helicopter):

 $\frac{165}{sin\left(22.2^o\right)}=\frac{y}{sin\left(26.7^o\right)}$165sin(22.2^o) =ysin(26.7^o)  

Isolating y:

 $y=165\times\frac{sin\left(26.7^o\right)}{sin\left(22.2^o\right)}=196.21\approx196m$y=165‍×sin(26.7^o)sin(22.2^o) =196.21≈196m 

Hence, the second person is aproximately 196 m away from the helicopter in a straight line.

Applying the sine law again to solve for z (or the distance between the first person caught in the avalanche and the helicopter), we have:

 $\frac{165}{sin\left(22.2^o\right)}=\frac{z}{sin\left(131.1^o\right)}$165sin(22.2^o) =zsin(131.1^o)  

  $z=165\times\frac{sin\left(131.1^o\right)}{sin\left(22.2^o\right)}\approx329m$z=165×sin(131.1^o)sin(22.2^o) ≈329m 

Hence, the first person is aproximately 329 m away from the helicopter in a straight line, while the second person is 196 m away fro the helicopter, also in a straight line.