## 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 ?     Explanation:

Using SOHCAHTOA, the sine of an angle is simply the length of the side opposite to it over the hypotenuse; however, we do not have the length of the hypotenuse yet.

Using the Pythagorean Theorem, we can solve for it:  So, the sine of this angle is: ### All ACT Math Resources 