How did they get a whole number from a decimal? Help!?

Question

The ratio of the opposite to the hypotenuse is .967 and defined to be the sine of the angle c = 75.5 degrees.

How did they find angle c from .967?

Other details: hypotenuse= 8 opposite=7.745 adjacent=2

When I enter sin^-1(0.968) into my calculator I get 1.317

What am I doing wrong?

Thanks Puzzling! My calculator was on radian mode. I would have NEVER figured that out.

Answer 1

Remember the mnemonic SOH-CAH-TOA, here you are using the SOH part:

sine = opposite / hypotenuse
sin(c) = 7.745 / 8
sin(c) = 0.968

Take the arcsin of both sides (inverse function to sin):
c = arcsin(0.968)
c ≈ 75.5°

You can use the 'arcsin' function on your calculator to get the angle c. It's also sometimes denoted 'sin^-1' meaning the inverse of sin. Be sure your calculator is in the correct DEG (degree) mode or else you'll get weird answers in radians.

Notice how you could have used CAH:
cosine = adjacent / hypotenuse
cos(c) = 2/8
cos(c) = 0.25
c = arccos(0.25)
c ≈ 75.5°

Whew, it comes out the same either way.

Answer 2

The sine of an angle in a right angled triangle is defined to be the ratio of the opposite to the hypotenuse so sin(75.5) = 0.968 (approx) NOTE 7.745 / 8 = 0.968 (approx) NOT 0.967

The angle c is found using the inverse sine function on your key pad

Answer 3

if the ratio of opposite to hypotenuse is 0.967, this is a sin relationship. Thus take the inverse sin of 0.967 sin^-1(0.967) and you should get 75.5 degrees.