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Right triangle calculator
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EXAMPLES
example 1:ex 1:
Find the hypotenuse of a right triangle in whose legs are $ a = 18~ cm $ and $ b = \dfrac{13}{2} cm $.
example 2:ex 2:
Find the angle $\alpha$ of a right triangle if hypotenuse $ c = 8~cm$ and leg $ a = 4~cm$.
example 3:ex 3:
Find the hypotenuse $ ~ c ~$ if $\alpha = 50^{\circ} $ and leg $ a = 8 $.
example 4:ex 4:
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:
| Pythagorean Theorem: | $$ a^2 + b^2 = c^2 $$ |  |
| Area: | $$ A = \frac{a b}{2} $$ | |
| Trig. functions: | $$ \sin \alpha = \frac{a}{c} $$ | |
| $$ \cos \alpha = \frac{b}{c} $$ | ||
| $$ \tan \alpha = \frac{a}{b} $$ |
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
Please tell me how can I make this better.
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