Right Triangle - Unknown Angle using Sine

\[\theta=\sin^{-1}\left(\frac{opposite}{hypotenuse}\right)\]

Variables

thetaunknown angle of the right triangle (rad or °)

oppositelength of the opposite side (m)

hypotenuselength of the hypotenuse (m)

Description

What is this formula?

This trigonometric formula calculates an unknown angle in a right triangle using the inverse sine function.

The sine ratio relates the opposite side of an angle to the hypotenuse. By applying the inverse sine function, the angle can be determined from known side lengths.

When to use it

Use this formula when:

- The opposite side is known

- The hypotenuse is known

- An acute angle must be calculated

- Solving right triangle problems

- Working with slopes, heights, or force components

The calculator may return the angle in degrees or radians depending on its configuration.

Example

If:

opposite = 6 m

hypotenuse = 10 m

Then:

theta = asin(6/10)

theta = asin(0.6)

theta ≈ 36.87°

Applications

- Trigonometry and geometry

- Engineering calculations

- Physics and mechanics

- Surveying and navigation

- Construction measurements

- Vector analysis