Right Triangle Side and Angle Calculator
Find the remaining sides and angle from one leg and its opposite angle.
Solve a right triangle when you know one leg and the angle across from it.
How the Math Works
This calculator leverages trigonometric relationships in right triangles to determine unknown sides and angles. Given one leg (a) and its opposite angle (A), the adjacent side (b) is calculated using the tangent ratio: b = a / tan(A). The hypotenuse (c) is derived from the sine ratio: c = a / sin(A). The remaining acute angle (B) is simply 90° minus angle A, since the sum of angles in a triangle is always 180° and one angle is already 90°.
Practical Applications
This tool is invaluable for professionals in construction, engineering, or surveying who need to calculate dimensions quickly. For example, if you know the height of a building (leg a) and the angle of elevation from the ground (angle A), you can determine the distance to the building's base (leg b) or the direct line-of-sight distance (hypotenuse c). It streamlines precision work where manual calculations might introduce errors or delays.
Day-to-Day Use
In everyday scenarios, this calculator helps with practical tasks like setting up ladders safely (ensuring proper angle and distance from a wall), designing garden beds with specific slopes, or adjusting furniture placement at exact angles. By simplifying trigonometry into an easy-to-use tool, it empowers DIY enthusiasts and homeowners to solve spatial problems confidently without needing advanced math skills.
Worked example
Leg 5 opposite 30° → b ≈ 8.66, c = 10, B = 60°.
FAQ
Why must A be under 90°?
A right triangle's other two angles are acute, so each is less than 90°.