I learned how to solve for a missing angle in a right triangle using trigonometry, specifically with the help of “SOH-CAH-TOA.” Mrs. Burton taught me.
Step 1: Label the sides of your triangle.
First, identify and label the sides of your right triangle. The longest side opposite the right angle is the hypotenuse (H). The side across from the angle you’re focusing on is the opposite (O), and the one next to the angle is the adjacent (A). This step ensures you’re set up to use the correct ratios.
Step 2: Choose the right trigonometric ratio.
Next, you need to decide which trigonometric function to use by applying SOH-CAH-TOA:
- SOH: Sine = Opposite / Hypotenuse
- CAH: Cosine = Adjacent / Hypotenuse
- TOA: Tangent = Opposite / Adjacent
Look at the two sides you’ve labeled. For example, if you have measurements for the opposite and adjacent sides, you’ll use the tangent ratio (TOA).
Step 3: Set up the equation.
Now that you’ve chosen the correct ratio, write down the corresponding formula. If you’re using tangent (TOA), for example, the equation would look like:
tan(θ)=O/A
Here, substitute the actual lengths for O and .
Step 4: Solve for the angle.
To find the angle θ, apply the inverse of the trigonometric function. For tangent, this would be:
θ=tan−1(O/A)
Use the inverse button on your calculator (often labeled as or “2nd”) to solve for the angle.
Step 5: Calculate the angle.
Finally, input the values into your scientific calculator. The result will likely be a decimal-round it to the nearest whole number, and indicate rounding by placing a small dot above the equal sign if needed.
And that’s how Mrs. Burton’s helped me find a missing angle using trigonometric ratios.