Right triangle calculator
Input any two values for a right triangle, and the calculator will find the unknown element.
The calculator provides a step-by-step explanation on how to calculate missing elements.
The calculator gives you a step-by-step
guide on how to find the missing value.
EXAMPLES
Find the hypotenuse of a right triangle in whose legs are $ a = 18~ cm $ and $ b = \dfrac{13}{2} cm $.
Find the angle $\alpha$ of a right triangle if hypotenuse $ c = 8~cm$ and leg $ a = 4~cm$.
Find the hypotenuse $ ~ c ~$ if $\alpha = 50^{\circ} $ and leg $ a = 8 $.
Find the area of a right triangle in which $\beta = 30^{\circ}$ and $b = \dfrac{5}{4} cm$
TUTORIAL
Right triangle calculations
The calculator uses the following formulas to find the missing values of a right triangle:
Example 01 :
Find hypotenuse $ c $ of a right triangle if $ a = 4\,cm $ and $ b = 8\,cm $.
Solution:
When we know two sides, we use the Pythagorean theorem to find the third one.
$$ \begin{aligned}
c^2 &= a^2 + b^2 \\[ 1 em]
c^2 &= 4^2 + 8^2 \\[ 1 em]
c^2 &= 16 + 64 \\[ 1 em]
c^2 &= 80 \\[ 1 em]
c &= \sqrt{80} \\[ 1 em]
c &= \sqrt{16 \cdot 5} \\[ 1 em]
c &= 4\sqrt{5}\\
\end{aligned}
$$
Example 02 :
Find the angle $\alpha$ of a right triangle if hypotenuse $ c = 14~cm$ and leg $ a = 8~cm$.
Solution:
In order to find missing angle we can use the sine function
$$ \begin{aligned}
\sin \alpha & = \frac{a}{c} \\[1 em]
\sin \alpha & = \frac{8}{14} \\[1 em]
\sin \alpha & = 0.5714 \\[1 em]
\alpha &= \sin^{-1} (0.5714) \\[1 em]
\alpha & \approx \, 39^{o}
\end{aligned}
$$
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