I got learnt about Trigonometry, including the concept of “SOH-CAH-TOA” and how it helps in solving right angled triangles.
Step 1: Label the sides of the triangle.
The first step is to identify and label the sides of the right triangle. The longest side, across from the right angle, is called the hypotenuse (H). The side directly across from the angle you’re working with is the opposite side (O), and the side next to that angle is the adjacent side (A).
Step 2: Pick the correct trigonometric function.
To decide which function to use, remember the acronym SOH-CAH-TOA:
- SOH stands for Sine, which is the ratio of the Opposite side over the Hypotenuse.
- CAH stands for Cosine, which is the ratio of the Adjacent side over the Hypotenuse.
- TOA stands for Tangent, which is the ratio of the Opposite side over the Adjacent side.
Look at the information you have, like side lengths or angles, and choose the function that fits the sides involved.
Step 3: Write out the equation.
Let’s say you’re using the sine function and the angle is 35 degrees. The equation would look like this:
sin(35∘)=x/10m
Here, is the unknown side you want to solve for, and 10 meters is the length of the hypotenuse.
Step 4: Solve for the variable.
To isolate the variable, multiply both sides by the length of the hypotenuse. In this case, it would be:
10×sin(35∘)=x
Step 5: Calculate the result.
Enter this equation into your calculator. For instance:
10×sin(35∘)=5.7m
This gives you the length of the missing side. And that’s how you can use trigonometric ratios to find unknown sides of a right-angled triangle!