What is the distance between A and B ?

Question

Points A and B are on opposite sides of the grand canyon. Point C is 200 yards from A. Angle B measures 87 degrees and angle C measures 67 degrees. What is the distance between A and B

Answer 1

Hi Madison, the law of sines says: A/sin A = B/sin B = C/sin C.

 

We know angle B, which is 87 degrees, and angle C, which is 67 degrees. We also know side AC of triangle ABC is 200 yards long. We are looking for side AB.

 

Then using the law of sines, we get:

 

Side AB is opposite angle C.

 

Equation:

 

AB/ sin 67 = 200/ sin 87

 

Solving for AB:

 

Multiply both sides by sin 67:

 

AB = 200 * sin 67 / sin 87

 

AB = 184.35 meters

 

The distance from point A to point B is 184.35 meters.

 

Questions?