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Right triangle calculator

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.

Find two sides of a triangle ABC if long leg b= $ \sqrt{ 38 }$ .

solution

Shorter leg $ a = \dfrac{\sqrt{ 114 }}{ 3 } $

Hypotenuse $ c = \dfrac{ 2 \sqrt{ 114}}{ 3 } $

explanation

Step 1: Find short leg a

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

$$ \begin{aligned} b &= \sqrt{3} \cdot a \\[1.3 em] \sqrt{ 38 } &= \sqrt{3} \cdot a \\[1.3 em] a &= \dfrac{ \sqrt{ 38 } }{ \sqrt{3}} \\[1.3 em] a &= \dfrac{ \sqrt{ 38 } }{ \sqrt{3}} \cdot \dfrac{\sqrt{3}}{\sqrt{3}} \\[1.3 em] a &= \frac{\sqrt{ 114 }}{ 3 } \end{aligned} $$

ID	Problem	Count
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Right triangle calculator

Find two sides of a triangle ABC if long leg b= $ \sqrt{ 38 }$ .

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