Question

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

Answer 1

Answer:

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

Step-by-step 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°

Answer 2

Answer: option c.

Step-by-step explanation:

You need to remember the identity:

$sin\alpha=\frac{opposite}{hypotenuse}$

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

 $\alpha =arcsin(\frac{opposite}{hypotenuse})$

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   $\alpha =arcsin(\frac{opposite}{hypotenuse})$

Then, you get:

$S=arcsin(\frac{31.4}{38.5})\\\\S=54.6\°$