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Right triangle calculator

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The right triangle calculator finds the missing area, angle, leg, hypotenuse and height of a triangle. The calculator also provides steps on how to solve the most important right triangles: the 30-60-90 triangle and the 45-45-90 triangle.

special triangle 45-45-90
Find two sides of a triangle ABC if hypotenuse c= $ 5$ .

solution

Shorter leg $ a = \dfrac{ 5 }{ 2 } $

Long leg $ b = \dfrac{ 5 \sqrt{ 3}}{ 2 } $

explanation

Step 1: Find short leg a

From the diagram above we can see that $ c = 2 \cdot a $. In this example we have:

$$ \begin{aligned} c &= 2 \cdot a \\[1.3 em] 5 &= 2 \cdot a \\[1.3 em] a &= \dfrac{ 5 }{ 2} \\[1.3 em] a &= \frac{ 5 }{ 2 } \end{aligned} $$

Step 2: Find long leg b

From the diagram above we can see that $ b = \sqrt{3} \cdot a $. In this example we have:

$$ b = \sqrt{3} \cdot \frac{ 5 }{ 2 } = \frac{ 5 \sqrt{ 3}}{ 2 } $$

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Script name : right-triangle-calculator

Form values: 2 , 5 , 55 , 1 , g , , , , , , , , , 1

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Special right triangle
Solve 30-60-90 and 45-45-90 triangles.
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Triangle type:
special triangle 30-60-90 special triangle 45-45-90
Provide one side of a right triangle
a =
b =
c =
 
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Triangle Calculator
Provide any two elements to get a third one.
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Solve for
Provide any two elements of a right triangle
a =
 
b =
c =
 
$ \alpha $ =
$ \beta $ =
 
A =
 
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