asa triangle -trig

[musicman]

i need help setting this one up!

" Radio direction finders are placed a points A and B, which are 3.46 miles apart on an east-west line, with A west of B. From A the bearing of a certain radio transmitter is 47.7degrees, and from B the bearing is 302.5degrees. find the distance of the transmitter from A."

please help.

 

[galactus]

It always helps to have a picture:

Angle A=90-47.7=42.3 degrees

Angle B=302.5-270=32.5 degrees

Angle C=180-(32.5+42.3)=105.2

Now, use the law of sines:

\(\displaystyle \frac{sinC}{c}=\frac{sinB}{b}\)

\(\displaystyle \frac{sin(105.2)}{3.46}=\frac{sin(32.5)}{b}\)

Solve for b.

 

[musicman]

thanks

thank you for the help