Question

Points A and B are on opposite sides of a lake. A point C is 81.3 meters from A. The measure of angle BAC is 78.33°, and the measure of angle ACB is determined to be 34.167°. Find the distance between points A and B (to the nearest meter).A. 25 mB. 49 mC. 35 mD. 54 m

Answer 1

B. 49m

Step-by-step explanation:

To find AB, we will use the sin rule. According to sine rule;

Cross multiply
`\begin{gathered} AB\sin 67.503\text{ = 81.3sin34.167} \\ 0.9239AB=45.66 \\ AB=(45.66)/(0.9239) \\ AB=49.42m \end{gathered}`Hence the distance between points A and B to the nearest meter is 49m