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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{ 93 }$ .

solution

Shorter leg $ a = \sqrt{ 31 } $

Hypotenuse $ c = 2 \sqrt{ 31 } $

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:

$$ \begin{aligned} b &= \sqrt{3} \cdot a \\[1.3 em] \sqrt{ 93 } &= \sqrt{3} \cdot a \\[1.3 em] a &= \dfrac{ \sqrt{ 93 } }{ \sqrt{3}} \\[1.3 em] a &= \dfrac{ \sqrt{ 93 } }{ \sqrt{3}} \cdot \dfrac{\sqrt{3}}{\sqrt{3}} \\[1.3 em] a &= \sqrt{ 31 } \end{aligned} $$

ID	Problem	Count
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22	Find the leg $ b $ of a right triangle if leg $a = 7$ and hypotenuse $c = 16$.	9
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36	Find the hypotenuse $ c $ of a right triangle if leg $a = 12$ and angle $\beta = 30^o$.	7
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38	Find the leg $ a $ of a right triangle if hypotenuse $c = 2$.	7
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48	Find the hypotenuse $ c $ of a right triangle if ???.	6
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50	Find the angle $ \beta $ of a right triangle if leg $a = 60$ and leg $b = 35$.	6

Right triangle calculator

Find two sides of a triangle ABC if long leg b= $ \sqrt{ 93 }$ .

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