Question

The Colonel spots a campfire at a bearing N 71 ∘ E from his current position. Sarge, who is positioned 235 feet due east of the Colonel reckons the bearing to the fire to be N 45 ∘ W from his current position. Determine the distance from the campfire to each man, rounded to the nearest foot.

Answer 1

Answer:

$X=85.123m$

$Y=184.88m$

Step-by-step explanation:

From the question we are told that:

Campfire Bearing from Colonel$x=N 71 \textdegree E$

Distance b/w Colonel and Sarge $Z=235feet$

Campfire Bearing from Sarge $y=N 45 \textdegree E$  

Generally the angles x' and y' are solved

$x'=90 \textdegree-71 \textdegree$

$x'=19 \textdegree$

$y'=90 \textdegree-45 \textdegree$

$y'=45 \textdegree$

Generally the angle z' is  solved

Sum of angles of a triangle is 180

Therefore

$z'=180 \textdegree-(19+45) \textdegree$

$z'=116 \textdegree$

Generally the sine rule equation for for all distances is mathematically given by

$\frac{Z}{sinz'}=\frac{X}{sinx'}=\frac{Y}{siny}$

Generally the the distance b/w the Colonel and the campfire X is mathematically given as

$\frac{235}{sin116}=\frac{X}{sinx'}$

$\frac{235}{sin116}=\frac{X}{sin19}$

$X=85.123m$

Generally the the distance b/w Sarge and the campfire X is mathematically given as

$\frac{235}{sin116}=\frac{Y}{siny}$

$\frac{235}{sin116}=\frac{Y}{sin45}$

$Y=184.88m$