Discover the famous relationship between the sides of a right triangle, and use it to find missing lengths.
In a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: (hypotenuse)² = (side 1)² + (side 2)².
A right triangle has legs of 3cm and 4cm. Find the hypotenuse.
3² + 4² = 9 + 16 = 25, so hypotenuse = √25 = 5cm
A right triangle has legs of 6cm and 8cm. Find the hypotenuse.
6² + 8² = 36 + 64 = 100, so hypotenuse = √100 = 10cm
If the hypotenuse and one leg are known, the other leg can be found by rearranging the theorem: (leg)² = (hypotenuse)² − (other leg)².
A right triangle has a hypotenuse of 13cm and one leg of 5cm. Find the other leg.
13² − 5² = 169 − 25 = 144, so the leg = √144 = 12cm
A ladder 10m long leans against a wall, with its base 6m from the wall. How high up the wall does it reach?
10² − 6² = 100 − 36 = 64, so the height = √64 = 8m
1. A right triangle has legs of 5cm and 12cm. Find the hypotenuse.
2. A right triangle has legs of 9cm and 12cm. Find the hypotenuse.
3. A right triangle has a hypotenuse of 17cm and one leg of 8cm. Find the other leg.
4. A right triangle has a hypotenuse of 25cm and one leg of 7cm. Find the other leg.
5. A rectangular field is 12m long and 5m wide. Find the length of its diagonal.