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The hypotenuse of the right triangle ABC shown below is 15 feet long. The sine of angle A is 3/5. How many feet long is AC?

The hypotenuse of the right triangle ABC shown below is 15 feet long. The sine of-example-1

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Answer:

12 feet

Explanation:

You want to know the length of AC in right triangle ABC when hypotenuse AB is 15 feet and sin(A) = 3/5.

Sine

The sine of angle A gives the relation between BC and AB:

Sin = Opposite/Hypotenuse

sin(A) = BC/AB

BC = AB·sin(A) = 15(3/5) = 9

Pythagorean theorem

The Pythagorean theorem can be used to find the length of side AC:

AC² +BC² = AB²

AC² +9² = 15²

AC = √(225 -81) = √144 = 12

The length of side AC is 12 feet.

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Additional comment

The ratio 3/5 tells you this is a 3-4-5 right triangle. They hypotenuse of 15 tells you the scale factor is 15/5 = 3. That means the ratios of lengths in this triangle are 9 ft : 12 ft : 15 ft. Side AC is the longer leg, 12 ft.

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