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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= $ 29 \sqrt{ 3 }$ .

solution

Shorter leg $ a = 29 $

Hypotenuse $ c = 58 $

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:

$$ \begin{aligned} b &= \sqrt{3} \cdot a \\[1.3 em] 29 \sqrt{ 3 } &= \sqrt{3} \cdot a \\[1.3 em] a &= \dfrac{ 29 \sqrt{ 3 } }{ \sqrt{3}} \\[1.3 em] a &= \dfrac{ 29 \sqrt{ 3 } }{ \sqrt{3}} \cdot \dfrac{\sqrt{3}}{\sqrt{3}} \\[1.3 em] a &= 29 \end{aligned} $$

ID	Problem	Count
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22	Find the leg $ a $ of a right triangle if hypotenuse $c = 37$ and angle $\alpha = 15^o$.	9
23	Find the hypotenuse $ c $ of a right triangle if leg $b = 39$ and angle $\beta = 60^o$.	9
24	Find the hypotenuse $ c $ of a right triangle if leg $a = 13$ and angle $\beta = 16^o$.	9
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36	Find the angle $ \alpha $ of a right triangle if leg $a = 4$ and leg $b = 9$.	7
37	Find the hypotenuse $ c $ of a right triangle if leg $a = 10$ and leg $b = 15$.	7
38	Find the leg $ a $ of a right triangle if hypotenuse $c = 7 \sqrt{ 2 }$ and angle $\beta = 45^o$.	7
39	Find the leg $ b $ of a right triangle if leg $a = 13$ and angle $\alpha = 76^o$.	7
40	Find the hypotenuse $ c $ of a right triangle if leg $a = 2$ and leg $b = 4$.	7
41	Find the leg $ a $ of a right triangle if leg $a = 12$ and hypotenuse $c = 15$.	7
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50	Find the leg $ b $ of a right triangle if hypotenuse $c = 5$ and angle $\alpha = 30^o$.	6

Right triangle calculator

Find two sides of a triangle ABC if long leg b= $ 29 \sqrt{ 3 }$ .

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