SOLUTION: Points A and B are on opposite sides of a lake. Point C is 83 meters from A. The measure of angle BAC is determined to be 99°, and the measure of angle ACB is determined to be 48Â

Algebra ->  Trigonometry-basics -> SOLUTION: Points A and B are on opposite sides of a lake. Point C is 83 meters from A. The measure of angle BAC is determined to be 99°, and the measure of angle ACB is determined to be 48      Log On


   

Question 1205056: Points A and B are on opposite sides of a lake. Point C is 83 meters from A. The measure of angle BAC is determined to be 99°, and the measure of angle ACB is determined to be 48°. What is the distance from A to B, rounded to the nearest whole meter?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


given:
A and B are on opposite sides of a lake
AC=b=83m
angle BAC or angle A=+99°
angle ACB or angle C=+48°
then angle B+=180-%2899%2B+48%29=33°

the law of sines states:
a%2Fsin%28A%29=b%2Fsin%28B%29=c%2Fsin%28C%29
let's start with
a%2Fsin%28A%29=b%2Fsin%28B%29
a%2Fsin%2899%29=83%2Fsin%2833%29
a=150.5
then
b%2Fsin%28B%29=c%2Fsin%28C%29
83%2Fsin%2833%29=c%2Fsin%2848%29
c=113.25

the distance from A to B, rounded to the nearest whole meter is 113m