SOLVE RIGHT TRIANGLE GUIDE
Right triangles in practical measurements
Right triangles connect horizontal distance, vertical distance, and a sloping or diagonal length. They are useful in design sketches, fabrication layouts, and everyday measurements when the two reference directions are perpendicular.
Find a rectangular panel’s diagonal
A rectangle’s width and height form the legs of a right triangle. Its diagonal is the hypotenuse.
Example: a panel 60 cm wide and 80 cm high
Diagonal = √(60² + 80²) = √10000 = 100 cm.
Use this relationship for a design dimension or to compare a measured diagonal. Measurement uncertainty still matters: a rounded width and height produce an approximate diagonal.
Find the angle of a slope
The angle above the horizontal is the inverse tangent of rise divided by horizontal run. Horizontal run is not the sloping surface length.
Sloping length = √(rise² + run²)
Example: rise of 0.6 m, run of 4 m
Angle = arctan(0.6 / 4) ≈ 8.53°.
Sloping length = √(0.6² + 4²) ≈ 4.0447 m. Rise / run × 100 gives a 15% slope, which is different from 15°.
Keep mixed units consistent
Convert the rise and run to the same unit before taking their ratio. For example, 60 cm / 4 m is 0.6 m / 4 m, not 60 / 4.
Solve Right Triangle accepts explicit units, including combined feet and inches, and converts them before calculating. Select the output unit you want for the results.
Separate geometry from project requirements
A geometrically correct slope does not establish accessibility compliance, load capacity, material allowances, or construction safety. The calculator provides dimensions; project standards and physical conditions require separate evaluation.
For fabrication, account for tolerances, tool accuracy, joints, and material thickness. Keep full precision during calculation and round to the precision appropriate for the actual measurement.
Try the rise-and-run exampleFormula reference
For an independent explanation of these relationships, see Pearson’s right triangle formulas and worked examples.
Related right triangle guides
- How to find the hypotenuse
- How to find a missing right triangle angle
- SOH CAH TOA, explained visually
- 30–60–90 and 45–45–90 triangles
- How to find a missing side of a right triangle
Open the right triangle calculator to check your own measurements.