Trigonometry Calculator
Solve right-angled triangles using trigonometric functions.
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Solving Right-Angled Triangles with Trigonometry
Our Trigonometry Calculator helps you find the missing sides and angles of a right-angled triangle by using the core principles of trigonometry (SOH CAH TOA).
What is a Trigonometry Calculator?
A Trigonometry Calculator is a tool designed to solve for the unknown sides and angles of a right-angled triangle. By providing just two known values (one side and one angle), it applies trigonometric functions like sine, cosine, and tangent to calculate all the remaining properties of the triangle, including side lengths, angles, area, and perimeter. It's an essential tool for students learning geometry and for professionals in fields like engineering and construction.
How It Works: Using SOH CAH TOA
The calculator uses the fundamental trigonometric ratios to solve the triangle:
sin(θ) = Opposite / Hypotenuse
cos(θ) = Adjacent / Hypotenuse
tan(θ) = Opposite / Adjacent
By rearranging these formulas based on the known side and angle, it can solve for the unknown sides. The second angle is found simply by knowing that all angles in a triangle must sum to 180°.
Frequently Asked Questions
What is trigonometry?
Trigonometry is a branch of mathematics that studies the relationships between the angles and side lengths of triangles. It's fundamental to geometry, physics, engineering, and many other fields.
What is SOH CAH TOA?
SOH CAH TOA is a mnemonic to remember the primary trigonometric ratios: Sine = Opposite / Hypotenuse, Cosine = Adjacent / Hypotenuse, and Tangent = Opposite / Adjacent. Our calculator uses these principles to solve for unknown sides.
How do you find a missing side of a right triangle?
If you know one angle (other than the 90° angle) and one side length, you can use trigonometric functions (sin, cos, tan) to find the lengths of the other two sides. For example, if you know the hypotenuse and an angle, you can find the opposite side using: Opposite = Hypotenuse × sin(angle).
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