This week, I have learned how to solve right triangle problems with SOH CAH TOA. This method can be used to find the missing angle or length. This method is convenient because you can find the answer quickly.

SOH CAH TOA

SOH CAH TOA is a rule for determining the sine, ratio, cosine ratio and tangent ratio for an angle in a right triangle.

In a right triangle, there are names for part of the triangle.

 

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The opposite, adjacent, and hypotenuse.

Opposite is the opposite side of the angle that you are looking for. If you are looking for the angle A, the opposite would be a. Opposite can NEVER be the long side of a triangle. In the case of the triangle above, opposite can’t be the part c.

Hypotenuse is always the longest side of the triangle. For the triangle above, the hypotenuse would be c since it is the longest side of the triangle.

Adjacent is the remaining part of the triangle. There are no ways to find the adjacent at the beginning if you don’t know the Opposite or the Hypotenuse.

 

Calculations

Now we know how to find the Opposite (O), Hypotenuse (H), and the Adjacent (A), we can now start the calculations.

SOH CAH TOA, for each method, you must know the 3 parts you want to know.

SOH: Sin(x)= Opposite/Hypotenuse

CAH: Cos(x)= Adjacent/Hypotenuse

TOA: Tan(x)= Opposite/Adjacent

The place where “x” is placed you must add the degree sign to signify that the angle is helping to solve the problem.

Calculations of length

In this triangle, we have lengths of the triangle and we have an angle.

First step is to find the 3 parts of the triangle. The opposite is 10 since angle 51 is across from it. The Hypnus is the h because it is the longest side of the triangle. The Adjacent is the part x since it is the remaining part of the triangle. If we want to know the part x, we need to use TOA, since we know the Opposite the O, Adjacent the A. We can’t use the other rules because they don’t include the rule that have the Opposite and the Adjacent. 

 

Tan(51 degree)= 10/x

10/Tan(51 degree)= x

8.10= x

I rounded to the nearest hundredths, as a result, the answer will become 8.10

 

Calculation of angle

To find the angle, we take the same steps, however we change for one step only.

If we were looking for the angle A, the Opposite would be 5 ft, Adjacent would be 12 ft, and Hypotenuse would be 13 ft.

Next would be writing the calculation. We can use any rules, since we know the 3 parts of the triangle and they are all in the part of SOH CAH TOA.

I’ll use SOH as an example.

Sin (A)= 5/13

Instead of using Sin, we use to find the angle. We use , ,  when we are looking for an angle.

A= 5/13 

A= 23

A would be 22.61986495…, however, we would usually round it to the decimal point. As a result, the answer would be 23.