SME
Grade 10 Math · Problem type
The 30°-60°-90° triangle
Use this for “The short leg of a 30°-60°-90° triangle is 5. Find the long leg and the hypotenuse.”
Diagram
30-60-90:
s
:
l
:
h
=
1
:
√
3
:
2
5
:
5
√
3
:
10
l
=
5
√
3
≈
8.66
This is an example. Type your own values to start a new problem.
l
=
s
3
h
Hypotenuse
calculated
Formulas
l
=
s
×
√
3
8.6603
=
5
×
√
3
h
=
2
×
s
10 = 2 × 5
Assumptions
•
A 30°-60°-90° triangle is half an equilateral triangle.
•
The short leg is across from 30°. The hypotenuse is twice it; the long leg is it times √3.
Step-by-step
WE KNOW
s = 5
FIND
long leg (l), hypotenuse (h)
Step 1 · Find long leg (l)
Use l = s × √3
The
long
leg
is
√
3
times
the
short
leg.
l
=
5
×
√
3
l
=
5
×
1.732
l
=
8.6603
(5
√
3
)
Step 2 · Find hypotenuse (h)
Use h = 2 × s
The hypotenuse is twice the short leg.
h
=
2
×
5
h
=
10
Check
Put the numbers back in. Both sides should match.
8.6603
≈
5
×
√
3
✓
10 = 2 × 5 ✓
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The 45°-45°-90° triangle
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Right-triangle trigonometry: sine, cosine and tangent
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