SOH CAH TOA is the phrase we use to determine the missing sides of a right-angle triangle. The CAH section of SOH CAH TOA is used to determine either the hypotenuse or adjacent sides of a triangle the equation is written as follows, Cosine = Adjacent/Hypotenuse. 

 

Example 1: 

By looking at the angle of this triangle we can determine that the missing side that we are solving for is the adjacent, and because we’re using cosine the hypotenuse will be the other side of the triangle that will be employed. Our equation will be written like this, . To solve this, we will star by multiplying the right and left sides of the equation by 16.5 to remove it from the right side. By doing this we are left with the equation . Now using a scientific calculator in the degree mode, we will type in . To determine X. The answer that should be displayed is 13.0, leaving us with the knowledge that x=13.0. 

 

Example 2: 

For this example, we can tell that the missing side of the triangle right angle is the hypotenuse. Because we are solving the equation using cosine the other side of the triangle, we will be using is the adjacent which is 1.9. We can also tell that the angle we are given is 64 degrees. Now we will write out our equation as follows, . For this equation “x” is on the bottom this is because cosine = adjacent/hypotenuse, and in this case, we are solving for the hypotenuse, unlike the equation above where we were solving for the adjacent side of the triangle. Now we must multiply both sides of the triangle by “x” to remove it from the right side of the equation. The equation we are left with should appear as this, . Now because we are solving for x we must get the cosine 64 to the left side of the equation. To do so we will divide both sides of the equation by cosine 64. Our equation should now look like, . After typing 1.9 divied by cosine 64 into our calculator we are left with 4.3, meaning that x = 4.3.