What Is FREE TOOLS Right Triangle Calculator?
A Right Triangle Calculator is a free online tool that helps you calculate the missing sides and angles of a right triangle. A right triangle is a triangle containing one 90° angle.
The calculator can use trigonometric functions such as sine, cosine, and tangent, as well as the Pythagorean Theorem, to solve unknown measurements.
What Is a Right Triangle?
Drag the points
40°
50°AdjacentOppositeHypotenuse
Angles 90°, 40°, and 50° include one fixed right angle
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A right triangle has three sides:
- Hypotenuse – the longest side, opposite the 90° angle.
- Opposite side – the side opposite the reference angle.
- Adjacent side – the side next to the reference angle, excluding the hypotenuse.
The two acute angles add up to: A+B=90∘A+B=90^\circ
Important Right Triangle Formulas
Pythagorean Theorem
When two sides are known: a2+b2=c2\boxed{a^2+b^2=c^2}
where cc is the hypotenuse.
Sine
sin(θ)=oppositehypotenuse\boxed{\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}}
Cosine
cos(θ)=adjacenthypotenuse\boxed{\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}}
Tangent
tan(θ)=oppositeadjacent\boxed{\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}}
These relationships are often remembered as SOH-CAH-TOA.
Example
Suppose a right triangle has:
- Opposite side = 6
- Adjacent side = 8
To find the hypotenuse: c=62+82c=\sqrt{6^2+8^2} c=36+64c=\sqrt{36+64} c=100=10c=\sqrt{100}=10
So the hypotenuse is 10 units.
The calculator can also determine the angles. For example: θ=tan−1(68)\theta=\tan^{-1}\left(\frac{6}{8}\right) θ≈36.87∘\theta\approx36.87^\circ
Therefore, the other acute angle is: 90∘−36.87∘=53.13∘90^\circ-36.87^\circ=53.13^\circ
What Can a Right Triangle Calculator Find?
A FREE TOOLS Right Triangle Calculator can calculate:
- Missing side lengths
- Hypotenuse
- Opposite side
- Adjacent side
- Missing angles
- Triangle area
- Triangle perimeter
- Trigonometric ratios
Depending on the calculator, you may only need to enter two known measurements to solve the remaining values.
How Does It Work?
Typically, you enter known values such as:
- One side and one angle
- Two sides
- The hypotenuse and one leg
- Two angles, where applicable
The calculator determines the unknown measurements using the appropriate geometric or trigonometric formula.
Why Use a Right Triangle Calculator?
It is useful for:
- Geometry homework
- Trigonometry exercises
- Construction and carpentry
- Architecture
- Engineering
- Surveying
- Finding diagonal distances
- Calculating heights and lengths
- Checking manual calculations
In Simple Terms
A FREE TOOLS Right Triangle Calculator makes it easy to solve a right triangle when some of its sides or angles are known.
It combines the Pythagorean Theorem, sine, cosine, and tangent to quickly calculate missing measurements.
Key formulas: a2+b2=c2\boxed{a^2+b^2=c^2} sin(θ)=oppositehypotenuse\boxed{\sin(\theta)=\frac{opposite}{hypotenuse}} cos(θ)=adjacenthypotenuse\boxed{\cos(\theta)=\frac{adjacent}{hypotenuse}} tan(θ)=oppositeadjacent\boxed{\tan(\theta)=\frac{opposite}{adjacent}}
A Right Triangle Calculator is therefore a convenient free tool for solving common geometry and trigonometry problems.
Keep working with right triangles
