Full solution

A B C

is a right-angled triangle.

\newline

Calculate the length of

B C

\newline

Give your answer correct to

1

decimal place.

Pythagoras' Theorem: We need to use Pythagoras' theorem, which is $a^2 + b^2 = c^2$ , where $c$ is the hypotenuse and $a$ and $b$ are the other two sides.
Plug in Values: Let's say we know the lengths of sides $AB$ and $AC$ . We can plug these values into the theorem to find $BC$ .
Calculate BC: Suppose $AB = 4\,\text{cm}$ and $AC = 3\,\text{cm}$ . Then we calculate $BC$ as follows: $BC^2 = AB^2 + AC^2$ .
Square Root: So, $BC^2 = 4^2 + 3^2 = 16 + 9 = 25$ .
Correcting Mistake: Now, we take the square root of both sides to find BC: $BC = \sqrt{25}.$
Correcting Mistake: Now, we take the square root of both sides to find $BC$ : $BC = \sqrt{25}$ . Calculating the square root, we get $BC = 5.0\,\text{cm}$ .
Correcting Mistake: Now, we take the square root of both sides to find BC: $BC = \sqrt{25}$ .Calculating the square root, we get $BC = 5.0\,\text{cm}$ .But wait, we made a mistake. Pythagoras' theorem is $c^2 = a^2 + b^2$ , not $a^2 + b^2 = c^2$ . We need to correct this.