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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

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 class=

Answer :

Answer:

B. 49m

Explanation:

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

[tex]\frac{AB}{\sinFirst, we need to get m78.33 + 34.167 + m112.497 + mmmSubstitute into the formula:[tex]\frac{AB}{\sin34.167}=\frac{81.3}{\sin 67.503}[/tex]Cross multiply[tex]\begin{gathered} AB\sin 67.503\text{ = 81.3sin34.167} \\ 0.9239AB=45.66 \\ AB=\frac{45.66}{0.9239} \\ AB=49.42m \end{gathered}[/tex]Hence the distance between points A and B to the nearest meter is 49m

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