Question

How would I set this problem up?
To find a distance across a lake, a surveyor locates points A, B, and C as shown. What is the measure of angle B to the nearest degree? (Enter only the number.) a=108 b= 55 C=59 degrees.
I know I can do the math, I just can’t remember how to set it up.

Answer 1

You have to show us the diagram. Use the "Draw" button below the reply box.

Answer 2

Use the law of cosines to find AB
Use the law of sines to find angle B

Answer 3

Law of cosines: c^2 = a^2 + b^2 - 2ab(cos(C))

Answer 4

so side AB would be 92.57?

Answer 5

Law of sines: sin(B) / b = sin(C) / c

Answer 6

and angle B would be 30.6 but rounded would be 31?

Answer 7

side AB = 92.58 is correct. I don't have a scientific calculator so I will have to do it online. Let me find the angle.

Answer 8

Yes angle B = 30.6 and round it up to 31.
Your calculations are all correct.

Answer 9

thank you much appreciated!

Answer 10

you are welcome.