How to Find the Base of a Right Angle Triangle

The right angle gets its own kind of triangle.

A right triangle, which is one with a right or 90-degree angle, shares the same properties as other triangles. Its area is still one-half the product of the base and height, but instead of height being a separate interior measurement, the height is one of its legs. Right triangles also have a special leg called a hypotenuse, which sits opposite the right angle. The length of the hypotenuse is computed by using the Pythagorean theorem, which its square equals the sum of the other legs squared. These two specialized properties, along with the general triangular perimeter, are the stepping stones in finding the measurement of the triangle's base leg.

Instructions

1. Double the area and then divide it by the height to calculate the base measurement if the area and height are known. For example, it the area is 30 and the height is 10, doubling 30 results in 60, and dividing that by 10 equals 6. The base is 6.

2. Subtract the height and hypotenuse measurements from the perimeter if the height, hypotenuse and perimeter are known. For example, the perimeter is 12, the height is 4 and the hypotenuse is 5. Summing 4 and 5 results in 9, and subtracting 9 from 12 results in 3. The base is 3.

3. Square the hypotenuse and square the height, then subtract the square of the height from the square of the hypotenuse, then determine the square root of the difference if the height and hypotenuse are known. For this example, the hypotenuse is 10 and the height is 8. Squaring 10 results in 100 and squaring 8 results in 64. Subtracting 64 from 100 results in 36, and the square root of 36 is 6. The base is 6.

References

• Interactive Maths Series Software: Area of a Right-Angled Triangle
• Math.com: Pythagorean Theorem and Right Triangle Facts
• CliffsNotes: Special Right Triangles