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.