Right Triangle Base and Angle from Height and Hypotenuse
Enter the height and hypotenuse to find the base, angle, and area. Solves a right triangle with the Pythagorean theorem and arcsine.
Input
Enter the height and hypotenuse of a right triangle to calculate the base, angle, and area.
Length unit (cm, m, etc.)
Length unit (cm, m, etc.)
Result
Base b
4
Angle opposite height θ
36.86989765 deg
Area
6
Height h
3
Hypotenuse c
5
Base b
4
Perimeter
12
Angle opposite height
36.86989765 deg
Other acute angle
53.13010235 deg
Lengths keep your input unit, area uses its square, and angles are shown in degrees.
How it works
- The base is found with the Pythagorean theorem: base equals the square root of hypotenuse squared minus height squared.
- The angle opposite the height is arcsine of height divided by hypotenuse, converted to degrees.
- The other acute angle equals 90 degrees minus the angle opposite the height.
- Area is base times height divided by 2, and perimeter is base plus height plus hypotenuse.
- The hypotenuse must be longer than the height. If it is equal or shorter, no triangle exists.
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Right Triangle Base and Angle from Height and Hypotenuse