Question

Using Pythagoras' theorem, calculate the length of the hypotenuse in this right-angled triangle. Give your answer in centimetres (cm) to 1 d.p. 4.2 cm 4 cm Not drawn accurately​

Answer 1

5.8 to 1 d.p

Explanation:

Let's use Pythagoras' theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (\(c\)) is equal to the sum of the squares of the lengths of the other two sides (\(a\) and \(b\)).

The formula is:

`{c }^(2) = {a}^(2) + {b}^(2)`

In your case, if one side is 4.2 cm and the other is 4 cm, let's call the hypotenuse "c".

`{c}^(2) = {(4.2)}^(2) + {(4)}^(2)`

`{c}^(2) = 17.64 + 16`

`{c}^(2) = 33.64`

Now, take the square root to find "c":

`c = √(33.64)`

`c = 5.8 \: cm \: (1 \: d.p)`

So, the length of the hypotenuse is approximately 5.8 cm to 1 d.p.