Question #135311
The bearing of a lighthouse from ship A is 29°NE and the bearing of that same lighthouse from ship B is 61°NW. If ship A and ship B are on the east-west line 200 km apart, how far is ship B from the lighthouse?
1
Expert's answer
2020-09-29T17:29:29-0400

Here is the sketch of the case above




Let the distance from the lighthouse to ship B be x.

Clearly from the figure above, a right-angle triangle if formed.

For us to find the value of x, we apply the trigonometric ratios of SOHCAHTOA, whereas we use the sine ratio;


sin(61°)=OppositeHypotenusesin (61°) = \frac{Opposite}{Hypotenuse}


sin(61°)=x200sin (61°) = \frac{x}{200}


x=200sin(61°)x = 200 sin (61°)


=174.92= 174.92


x=174.92kmx= 174.92 km


Therefore, the distance from ship B to the lighthouse is 174.92km174.92 km


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS