Find 𝑥 in the right triangle shown.
In order to calculate a missing length in a right-angled triangle, we need to use Pythagoras’s theorem. This states that 𝑎 squared plus 𝑏 squared equals 𝑐 squared. Well, length 𝑐 is the hypotenuse or longest side of the triangle. This will always be found opposite the right angle. In this question, the hypotenuse is 𝑥.
Substituting in the values from the triangle gives us an equation four squared plus three squared equals 𝑥 squared. Four squared is equal to 16 and three squared is equal to nine. Therefore, 16 plus nine must be equal to 𝑥 squared. 16 plus nine is 25. Therefore, 𝑥 squared is equal to 25.
Square rooting both sides of this equation gives us 𝑥 equals five, as the square root of 25 is five and the square root of 𝑥 squared is 𝑥. This means that the missing length 𝐴𝐵 in the right triangle is 𝑥 equals five.