Apply the Pythagoras theorem to right-angled triangles, and use its converse to test whether a triangle is right-angled.
In a right triangle, a²+b²=c², where c is the hypotenuse. This is used to find missing sides.
A right triangle has legs 9 cm and 12 cm. Find the hypotenuse.
c²=81+144=225; c=15 cm
A ladder 13 m long leans against a wall, base 5 m from the wall. How high does it reach?
height²=13²−5²=169−25=144; height=12 m
A right triangle has legs 20 cm and 21 cm. Find the hypotenuse.
√(400+441)=√841=29 cm
If a²+b²=c² for a triangle's sides, then the triangle is right-angled, with the right angle opposite side c.
A triangle has sides 8, 15, 17. Is it right-angled?
8²+15²=64+225=289=17², so yes, it's right-angled
A triangle has sides 5, 7, 9. Is it right-angled?
5²+7²=25+49=74, and 9²=81; since 74≠81, it's not right-angled
A triangle has sides 9, 12, 15. Is it right-angled?
9²+12²=81+144=225=15², so yes, it's right-angled
1. A right triangle has legs 6 cm and 8 cm. Find the hypotenuse.
2. A right triangle has hypotenuse 25 cm and one leg 7 cm. Find the other leg.
3. Is a triangle with sides 7,24,25 right-angled?
4. Is a triangle with sides 4,5,6 right-angled?
5. A rectangular field is 30 m long and 40 m wide. Find the length of its diagonal.
6. A right triangle has legs 5 cm and 12 cm. Find the hypotenuse.
7. A right triangle has hypotenuse 41 cm and one leg 9 cm. Find the other leg.
8. Is a triangle with sides 6,8,10 right-angled?
9. Is a triangle with sides 5,6,7 right-angled?
10. A ladder 17 m long leans against a wall, its base 8 m from the wall. How high does it reach?