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.
solution
Shorter leg $ a = \dfrac{ 137 \sqrt{ 3}}{ 125 } $
Hypotenuse $ c = \dfrac{ 274 \sqrt{ 3}}{ 125 } $
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:
$$ \begin{aligned} b &= \sqrt{3} \cdot a \\[1.3 em] \frac{ 411 }{ 125 } &= \sqrt{3} \cdot a \\[1.3 em] a &= \dfrac{ \frac{ 411 }{ 125 } }{ \sqrt{3}} \\[1.3 em] a &= \dfrac{ \frac{ 411 }{ 125 } }{ \sqrt{3}} \cdot \dfrac{\sqrt{3}}{\sqrt{3}} \\[1.3 em] a &= \frac{ 137 \sqrt{ 3}}{ 125 } \end{aligned} $$Step 2: Find hypotenuse c.
From the diagram above we can see that $ c = 2 \cdot a $. In this example we have:
$$ c = 2 \cdot \frac{ 137 \sqrt{ 3}}{ 125 } = \frac{ 274 \sqrt{ 3}}{ 125 } $$