This week in math I learned how to use the sine of a triangle to find either the hypotenuse or opposite side of a triangle. A triangle has three sides,  the longest side of a triangle is called the hypotenuse. The other two sides of the triangle are called the opposite and the adjacent. If the triangle has a marked angle the side across from it would be the opposite, leaving the unmarked side the adjacent.  

To find the sine of a triangle you can use the saying, SOH CAH TOA. The SOH in SOH CAH TOA stands for sine= . So in order to find an angle with the sine of a triangle we would already need to know the given angle (sine) of a triangle and either the hypotenuse or opposite side of a triangle as well. 

Example 1: 

In this example we are given the sine, which is 15 degrees, and the hypotenuse, which is 12, so we are solvng for x which is the opposite side of the triangle. To solve this equation I first write it out as . In order to get x all alone I would times by 12, allowing the 12s to cancel each other out, and because anything done to one side of an equation has to be done to the other side I would rewrite the equation as x=12sin15. Next I would use my calculator and be sure to put it in the degree setting. I would then select the number 12 and then sine, it would appear as sin on a calculator and 15. My calculator would then multiply 12 by sine 15 leaving me with the number x=3.1058. 

Example 2:

In this example sine is 55 degrees and we know our opposite length, 65, and the unknown length we are solving for is the hypotenuse. In order to solve this equation we must first begin by writing . We would then multiply $latex\frac{65}{x}$ by x which would leave us with 65, but we must remember that everything done to one side of an equation must be done to the other making our equation, x multiplied by sine55 = 65. We now need to isolate x and to do this we must divide sin55 by itself and the 65. . We then would use our scientific calculator in the degree setting to do 65 divided by sin55. Our final answer would be x=79.3503.