Question

HELP!!

If theta is the smallest angle in a right triangle with side lengths of 3,4, and 5 units, then what does sin(theta) equal?

3/4
3/5
4/5
5/3

Answer 1

It is 3/5, because, sin is opposite over hypotenuse. If you are finding the smallest angle, then opposite would be 3 (the smallest side) over 5 (the hypotenuse)

Answer 2

3/5

Explanation:

Givens

• The right triangle has side lengths of 3, 4 and 5.

• Angle theta is the smallest angle.

From this information, we can deduct that the hypothenuse is 5 units long, and legs are 3 and 4 units long.

So, if theta is the smallest angle, then

`sin\theta=(3)/(5)`

Because this relation gives the following angle

`\theta = sin^(-1)((3)/(5) )\approx 37\°`

Which is the smallest angle, because the other one is

`\alpha=sin^(-1)=(4)/(5)\approx 53\°`

Therefore, the right answer the second choice.