Right triangle calculator

problem

Find angle $ \alpha $ of a right triangle if leg $a = 4$ and leg $b = 8$.

solution

$$ \alpha \approx 26.5651^o $$

explanation

To find angle $ \alpha $ use formula:

$$ \tan \left( \alpha \right) = \dfrac{ a }{ b } $$

After substituting $ a = 4 $ and $ b = 8 $ we have:

$$ \tan \left( \alpha \right) = \dfrac{ 4 }{ 8 } $$ $$ \tan \left( \alpha \right) = \frac{ 1 }{ 2 } $$ $$ \alpha = \arctan\left( \frac{ 1 }{ 2 } \right) $$ $$ \alpha = 26.5651^o $$

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Script name : right-triangle-calculator

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Enter two values of a right triangle and select what to find.
The calculator gives you a step-by-step guide on how to find the missing value. Calculator works with decimal numbers, fractions and square roots.
show help ↓↓ examples ↓↓ tutorial ↓↓
The missing value is:
Provide any two values of a right triangle
calculator works with decimals, fractions and square roots (to input $ \color{blue}{\sqrt{2}} $ type $\color{blue}{\text{r2}} $)
leg $ a $
=
leg $ b $
=
hyp. $ c $
=
angle $ \alpha $
=
angle $\beta$
=
Area $ A $
=
working...
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: $$ a^2 + b^2 = c^2 $$ right triangle
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

$$ \begin{aligned} \sin \alpha & = \frac{a}{c} \\[1 em] \sin \alpha & = \frac{8}{14} \\[1 em] \sin \alpha & = 0.5714 \\[1 em] \alpha &= \sin^{-1} (0.5714) \\[1 em] \alpha & \approx \, 39^{o} \end{aligned} $$
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