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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 hypotenuse c= $ \frac{ 253 }{ 2 }$ .

solution

Shorter leg $ a = \dfrac{ 253 }{ 4 } $

Long leg $ b = \dfrac{ 253 \sqrt{ 3}}{ 4 } $

explanation

Step 1: Find short leg a

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

$$ \begin{aligned} c &= 2 \cdot a \\[1.3 em] \frac{ 253 }{ 2 } &= 2 \cdot a \\[1.3 em] a &= \dfrac{ \frac{ 253 }{ 2 } }{ 2} \\[1.3 em] a &= \frac{ 253 }{ 4 } \end{aligned} $$

ID	Problem	Count
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11	Find the leg $ b $ of a right triangle if leg $a = 4$ and angle $\beta = 50^o$.	10
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18	Find the hypotenuse $ c $ of a right triangle if leg $a = 4$ and angle $\beta = 50^o$.	9
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21	Find the hypotenuse $ c $ of a right triangle if leg $a = 13$ and angle $\beta = 16^o$.	9
22	Find the leg $ b $ of a right triangle if leg $a = 7$ and hypotenuse $c = 16$.	9
23	Find the leg $ a $ of a right triangle if leg $b = 10$ and hypotenuse $c = 20$.	9
24	Find the angle $ \beta $ of a right triangle if leg $a = \frac{ 37 }{ 2 }$ and hypotenuse $c = \frac{ 229 }{ 10 }$.	9
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26	Find the angle $ \beta $ of a right triangle if leg $a = \sqrt{ 39 }$ and leg $b = \sqrt{ 33 }$.	8
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28	Find the angle $ \beta $ of a right triangle if leg $a = 7$ and hypotenuse $c = 16$.	8
29	Find the leg $ a $ of a right triangle if leg $b = 16$ and angle $\alpha = 37^o$.	8
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33	Find the leg $ b $ of a right triangle if leg $a = \frac{ 37 }{ 2 }$ and hypotenuse $c = \frac{ 229 }{ 10 }$.	8
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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 hypotenuse c= $ \frac{ 253 }{ 2 }$ .

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