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# 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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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: $$a^2 + b^2 = c^2$$ 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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