The calculator uses the following formulas to find the missing values of a right triangle:
Pythagorean Theorem: | $$ a^2 + b^2 = c^2 $$ | ![]() |
Area: | $$ A = \frac{a b}{2} $$ | |
Trig. functions: | $$ \sin \alpha = \frac{a}{c} $$ | |
$$ \cos \alpha = \frac{b}{c} $$ | ||
$$ \tan \alpha = \frac{a}{b} $$ |
Find hypotenuse $ c $ of a right triangle if $ a = 4\,cm $ and $ b = 8\,cm $.
When we know two sides, we use the Pythagorean theorem to find the third one.
$$ \begin{aligned} c^2 &= a^2 + b^2 \\[ 1 em] c^2 &= 4^2 + 8^2 \\[ 1 em] c^2 &= 16 + 64 \\[ 1 em] c^2 &= 80 \\[ 1 em] c &= \sqrt{80} \\[ 1 em] c &= \sqrt{16 \cdot 5} \\[ 1 em] c &= 4\sqrt{5}\\ \end{aligned} $$Find the angle $\alpha$ of a right triangle if hypotenuse $ c = 14~cm$ and leg $ a = 8~cm$.
In order to find missing angle we can use the sine function
$$ \begin{aligned} \sin \alpha & = \frac{a}{c} \\[1 em] \sin \alpha & = \frac{8}{14} \\[1 em] \sin \alpha & = 0.5714 \\[1 em] \alpha &= \sin^{-1} (0.5714) \\[1 em] \alpha & \approx \, 39^{o} \end{aligned} $$Please tell me how can I make this better.