Question

If t=38.5 and s=31.4 find S. Round to the nearest tenth

Answer 1

Answer: option c.

Explanation:

You need to remember the identity:

`sin\alpha=(opposite)/(hypotenuse)`

The inverse of the sine function is arcsine. You need to use this to calculate the angle "S":

`\alpha =arcsin((opposite)/(hypotenuse))`

You know that you need to find the measure of "S" and
`t=38.5` (which is the hypotenuse) and
`s=31.4` (which is the opposite side), then you can substitute values into
`\alpha =arcsin((opposite)/(hypotenuse))`

Then, you get:

`S=arcsin((31.4)/(38.5))\\\\S=54.6\°`

Answer 2

The correct answer option is C. S = 54.6°.

Explanation:

We are given a right angled triangle with two known sides,
`s` and
`t`.

We are to find the value of the angle
`S`.

For that, we will use sine.

`sin S = \frac { s } { t }`

`sin S = \frac { 3 1 . 4 } { 3 8 . 5 }`

`S = sin'0.815`

S = 54.6°