ACT Math : How to find the sine of a missing side

Example Questions

Example Question #1 : How To Find The Sine Of A Missing Side

In the triangle below,  units and  units. What is ?

Explanation:

Because , we need to first find the length of BC.

Using the Pythagorean theorem,

.

Example Question #2 : How To Find The Sine Of A Missing Side

What is the value of  in the triangle above? Round to the nearest hundredth.

Explanation:

We know that the sine of an angle is:

Therefore, we can write for this question:

This allows us to solve for  easily:

Rounding, this gives us .

Example Question #3 : How To Find The Sine Of A Missing Side

A right triangle has leg lengths  and . What is the sine of the angle opposite from the side of length ?