Pythagoras' Theorem

A right-angled triangle has shorter sides $6$ and $8$. Find the hypotenuse.

• 1Apply the theorem: $c^2=a^2+b^2=6^2+8^2$
• 2Work out the squares: $36+64=100$
• 3Take the square root: c = √$100=10$

Answer: $10$

A right-angled triangle has hypotenuse $13$ and one shorter side $5$. Find the other shorter side.

• 1Rearrange: $b^2=c^2-a^2=13^2-5^2$
• 2Work out the squares: $169-25=144$
• 3Take the square root: b = √$144=12$

Answer: $12$

A right-angled triangle has shorter sides $5$ and $7$. Find the hypotenuse, to $2$ decimal places.

• 1$c^2=5^2+7^2=25+49=74$
• 2c = √$74$ ≈ $8.60$

Answer: $8.60$ (to $2$ decimal places)