4.9 B) Not Finding the Hypotenuse
We are now going to have a look at a few examples where we will be given the hypotenuse and one of the other sides of the right-angled triangle and asked to find the length of the other side. To find this unknown length, we will just rearrange the standard Pythagoras’ theorem formula to make one of the lengths that is not the hypotenuse the subject. I am going to make a2 the subject. The standard formula is given below.
In order to make a2 the subject, we need to move the b2 from the left side of the equation to the right. We are able to do by doing the opposite; we take b2 from both sides of the equation.
What is the length of the unknown side? Give your answer to one decimal place.
We now need to square root because we are looking for the value of a and not a2.
What is the length of the unknown side in the right-angled triangle below? Give your answer to one decimal place.
We now need to square root because we are looking for the value of a and not a2.
I think that the best way to remember Pythagoras’ theorem is to label the hypotenuse of the right-angled triangle straight away. The hypotenuse is the longest side and the side that is opposite to the right angle in the triangle. I would always label this side independently of whether it is the side that I am looking for or the side that I am given.
The next step is to identify what side I am looking for.
- If I am looking for the hypotenuse of the triangle, we find the square of the hypotenuse by adding the squares of the other two non-hypotenuse sides together.
- If I am looking for the length of a side that is not the hypotenuse, we find the square of the side that we are looking for by taking the square of the side that we are given that is not the hypotenuse from the square of the hypotenuse.
Another tip is to tilt your head, or the page so that the triangle is easier to work with.
There are a lot of Pythagoras’ theorem question in the quiz, so give them a go and see how you get on.