How to find the missing side of a right triangle
- Enter any two sides. Side a and Side b are the two sides that meet at the right angle, and Hypotenuse c is the long side opposite it.
- Leave the side you want to find empty.
- Read the missing side with the sum used, then the triangle's area, perimeter and its three angles.
Worked example and the 3-4-5 rule
With the default sides of 6 and 8, the hypotenuse is √(6² + 8²) = √100 = 10. The calculator also shows:
- Area: 6 × 8 ÷ 2 = 24
- Perimeter: 6 + 8 + 10 = 24
- Angles: 36.8699°, 53.1301° and 90°
6, 8, 10 is the 3, 4, 5 triangle doubled. Builders use that to check a corner is square: measure 3 units along one wall and 4 along the other, and the diagonal between the marks should be exactly 5. Any multiple works, such as 6, 8, 10 feet or 0.9, 1.2, 1.5 metres, and a bigger triangle gives a more accurate check.
Whole-number sets like this are called Pythagorean triples. Other common ones are 5, 12, 13, then 8, 15, 17 and 7, 24, 25.
Everyday uses
- Ladders. A 5 m ladder with its foot 1.5 m from the wall reaches √(5² − 1.5²) = √22.75, about 4.77 m up the wall.
- Screen sizes. A screen’s size is its diagonal. A screen 24 inches wide and 13.5 inches high has a diagonal of √(576 + 182.25), about 27.5 inches.
- Ramps and roofs. The sloping length of a ramp that rises 0.5 m over 6 m is √(36.25), about 6.02 m.
- Distances on a map grid. 3 km east and 4 km north is 5 km in a straight line.
In each case the two sides you know must be at right angles to each other. For triangles without a right angle you need the law of cosines instead.