Question

What is the trigonometric ratio for sin C?

Answer 1

Answer:  9/41

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Explanation:

We have a triangle with these three sides.

• a = 80
• b = unknown
• c = 82

Use the pythagorean theorem to find b

a^2+b^2 = c^2

b = sqrt(c^2 - a^2)

b = sqrt(82^2 - 80^2)

b = sqrt(324)

b = 18

This is the missing vertical leg of the triangle. And this is also the side opposite angle C.

We have enough information to compute the sine of the angle.

sin(angle) = opposite/hypotenuse

sin(C) = AB/AC

sin(C) = 18/82

sin(C) = (9*2)/(41*2)

sin(C) = 9/41