Hypotenuse — Grade 7 Math, what it means and where it is taught
The side opposite the right angle — always the longest.
Taught in Grade 7 Math.
Where it is taught
What uses it later
This idea is needed for:
- Hypotenuse-Leg — HL: for right triangles only, a matching hypotenuse and one leg are enough.
- Adjacent — The side next to that angle which is not the hypotenuse.
- Sine — sin θ = oppositehypotenuse.
- Cosine — cos θ = adjacenthypotenuse.
Practise this idea
21 questions in the course bank use Hypotenuse, in Pythagorean Theorem, Distance on the Coordinate Plane, Triangle Congruence Proofs, Right Triangle Trigonometry. The first 8 are below; the rest are in those units.
Problem 1
A right triangle has legs 3 and 4. Find the hypotenuse.
Worked answer
5
9 + 16 = 25
c = √25 = 5
Problem 2
A right triangle has legs 6 and 8. Find the hypotenuse.
Worked answer
10
36 + 64 = 100
c = 10
Problem 3
A right triangle has legs 5 and 12. Find the hypotenuse.
Worked answer
13
25 + 144 = 169
c = 13
Problem 4
A right triangle has hypotenuse 13 and one leg 5. Find the other leg.
Worked answer
12
169 - 25 = 144
√144 = 12
Problem 5
Which side of a right triangle is the hypotenuse?
- The shortest side
- The side opposite the right angle
- Either of the two legs
Worked answer
The side opposite the right angle
The hypotenuse is opposite the right angle, and always the longest side.
Problem 6
A right triangle has legs 9 and 12. Find the hypotenuse.
Worked answer
15
81 + 144 = 225
c = 15
Problem 7
A 17 ft ladder leans against a wall with its foot 8 ft from the base. How high up the wall does it reach?
Worked answer
15
289 - 64 = 225
√225 = 15 ft
Problem 8
A right triangle has legs 8 and 15. Find the hypotenuse.
Worked answer
17
64 + 225 = 289
c = 17