Right Triangle - Unknown Side using Sine

\[opposite=hypotenuse\sin(\theta)\]

Variables

oppositelength of the opposite side (m)

hypotenuselength of the hypotenuse (m)

thetaknown angle of the right triangle (rad or °)

This trigonometric formula calculates the opposite side of a right triangle using the sine ratio.

The sine function relates the opposite side of an angle to the hypotenuse of the triangle.

It is one of the most commonly used formulas in trigonometry, physics, engineering, and geometry.

Use this formula when:

- The hypotenuse is known

- One acute angle is known

- The opposite side must be calculated

- Solving right triangle problems

- Working with slopes, elevations, or force components

The angle can be expressed in degrees or radians depending on the calculator settings.

If:

hypotenuse = 12 m

theta = 40°

Then:

opposite = 12*sin(40°)

opposite ≈ 7.71 m

- Trigonometry and geometry

- Structural engineering

- Physics and mechanics

- Navigation and surveying

- Construction calculations

- Vector decomposition