Show Enter two values of a right triangle and select what to find. show help ↓↓ examples ↓↓ tutorial ↓↓ The missing value is: Provide any two values of a right triangle leg $ a $ = leg $ b $ = hyp. $ c $ = angle $ \alpha $ = angle $\beta$ = Area $ A $ = 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 calculationsThe 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 $$ \begin{aligned} \sin \alpha & = \frac{a}{c} \\[1 em] \sin \alpha & = \frac{8}{14} \\[1 em] \sin \alpha & = 0.5714 \\[1 em] \alpha &= \sin^{-1} (0.5714) \\[1 em] \alpha & \approx \, 39^{o} \end{aligned} $$ Search our database of more than 200 calculators 228 168 076 solved problems Angle and hypotenuse of right triangle
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