Special Right Triangles Calculator
MathCalculate all sides, perimeter, and area of a 45-45-90, 30-60-90, or 3-4-5 right triangle from one base measurement.
Side A
First leg of the triangle.
Side B
5.0000
Second leg of the triangle.
Hypotenuse
7.0711
Hypotenuse of the triangle.
Perimeter
17.0711
Total perimeter.
Area
12.5000
Triangle area.
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Odeh Ahwal0people find this calculator helpful
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Creators
Odeh Ahwal0people find this calculator helpful
Views
Helpful
Saved
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Frequently Asked Questions
What does the base measurement represent for each type?
For 45-45-90, it is the length of either equal leg. For 30-60-90, it is the shorter leg, opposite the 30 degree angle. For 3-4-5, it is the scale unit, so a value of 5 gives sides of 15, 20, and 25.
Why are these called special right triangles?
Their side ratios are fixed and well known: 45-45-90 has sides in ratio 1:1:root 2, 30-60-90 has ratio 1:root 3:2, and 3-4-5 is the simplest whole-number Pythagorean triple. Knowing the ratio lets you find every side from just one measurement.
Is 3-4-5 a right triangle even though it has no special angles listed?
Yes, any triangle whose sides satisfy the Pythagorean theorem, 3 squared plus 4 squared equals 5 squared, is a right triangle, even though its angles are not the round numbers 45 or 30-60 degrees seen in the other two special cases.
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