# Pythagoras vs. Trigonometry: Which One Should I Use?

Pythagoras and trigonometry (basic) both work in right angled triangles. In this article you will be shown how to choose the correct one.

Pythagoras is used when you have a right angled triangle and you need to work out one of the missing side lengths. In order to do this you will need to know two of the other side lengths. Pythagoras is only to do with the sides of a right angled triangle.

Trigonometry on the other hand can be used to calculate a missing side or a missing angle in a right angled triangle. If you are asked to find a side length then you will need to be given a side length and an angle (not including the right angle). If you are finding an angle then you will need to know the lengths of 2 sides of the right angled triangle.

Let’s take a look at some examples:

**Example 1**

Work out ?

Here you need to use trigonometry as you need to work out a missing side and you are give one of the sides and one of the angles:

Sin? = O/H (use sin as you are given the hypotenuse and you finding the opposite side)

Sin63 = ?/6.2 (sub your values into your formula)

? = 6.2 × Sin63 (since you are dividing ? by 6.2 you need to multiply sin63 by 6.2)

? = 5.2 cm (rounded to 1 decimal place)

**Example 2**

Work out ?

In this example you need to work out a side length. Since you know the side lengths of two of the other sides then this is a Pythagoras question.

a² + b² = c²

?² + 9² = 10² (you are not finding the longest side(c) so take care when subbing your values)

?² + 81 = 100

?² = 19 (now square root)

? = 4.4 cm to 1 decimal place

**Example 3**

Work out ?

In this example you need to work out the angle and you are given 2 side lengths. Therefore you need to use trigonometry:

Cos ? = A/H (used cosine as you have the Adjacent and Hypotenuse).

Cos ? = 9/11 (sub your number into the formula)

? = Cos^{-1}(9/11) (Use inverse cos as this is the inverse operation to cos)

? = 35.1⁰ (rounded to 1 decimal place)

## Questions & Answers

**Question:** How do you know when to add or subtract when working with a triangle in math?

**Answer:** You only add the two numbers if you are finding the longest side of the right angled triangle.

If you are having trouble finding the longest side it will always be opposite the right angle.