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Points A and B are on opposite sides of a lake. A point C is 105.6 meters from A. The measure of ∠BAC is 70.5°, and the measure of ∠ACB is determined to be 38.833°. Find the distance between points A and B (to the nearest meter).

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smmwaite

Answer:

= 70 Meters

Step-by-step explanation:

We can use the sine rule as follows:

Angle ABC=180-(70.5+38.833)

=70.667°

Using the sine rule and sides AB, AC and angles ABC and ACB:

b/Sin B=c/Sin C

Replacing with the values above we get:

AC/Sin ABC= AB/Sin ACB

105.6/Sin 70.667=AB/Sin 38.833

AB=(105.6 Sin 38.833)/Sin 70.667

=70.17 meters

The distance between the two points to the nearest meter is 70 meters

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