SME
Grade 10 Math · Problem type
The 45°-45°-90° triangle
Use this for “A leg of a 45°-45°-90° triangle is 7. How long is the hypotenuse?”
Diagram
45-45-90:
s
:
s
:
c
=
1
:
1
:
√
2
7
:
7
:
7
√
2
c
=
7
√
2
≈
9.9
This is an example. Type your own values to start a new problem.
c
=
s
2
Formulas
c
=
s
×
√
2
9.8995
=
7
×
√
2
Assumptions
•
A 45°-45°-90° triangle is half a square: its two legs are equal.
•
So c² = s² + s² = 2s², and the hypotenuse is a leg times √2.
•
Going back, a leg is the hypotenuse ÷ √2.
Step-by-step
WE KNOW
s = 7
FIND
hypotenuse (c)
Step 1 · Find hypotenuse (c)
Use c = s × √2
The
hypotenuse
is
√
2
times
a
leg.
c
=
7
×
√
2
c
=
7
×
1.414
c
=
9.8995
(7
√
2
)
Check
Put the numbers back in. Both sides should match.
9.8995
≈
7
×
√
2
✓
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The Pythagorean theorem's converse and special right triangles
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The 30°-60°-90° triangle
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Pythagorean theorem and distance between points
Exponent properties, rational exponents, simplifying radicals, and rational and irrational numbers