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, $x$ 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!

Scientific Notation – Large numbers example:

Let’s say we have a number like 9,300,000. In Standard Notation, that’s the number we would write out in full, but in Scientific Notation, it becomes 9.3 x 10⁶. Here’s how it works: you place the decimal between the 9 and the 3, because the first part (the “coefficient”) has to be a number between 1 and 10. After that, the exponent (6) tells us how many places the decimal moved from its original position to get to this format. So in this case, the decimal moves 6 places to the left to get from 9,300,000 to 9.3.

Scientific Notation – Small numbers example:

For smaller numbers, it’s a similar process, but we move in the opposite direction. For example, if we have 0.00047, the Scientific Notation would be 4.7 x 10⁻⁴. We moved the decimal 4 places to the right this time, and because we moved to the right, the exponent is negative. Just like before, the coefficient (4.7) has to be a number between 1 and 10. So, 4.7 x 10⁻⁴ is a more compact way to write 0.00047.