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 = 600 \sqrt{ 3 } $
Hypotenuse $ c = 1200 \sqrt{ 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:
$$ \begin{aligned} b &= \sqrt{3} \cdot a \\[1.3 em] 1800 &= \sqrt{3} \cdot a \\[1.3 em] a &= \dfrac{ 1800 }{ \sqrt{3}} \\[1.3 em] a &= \dfrac{ 1800 }{ \sqrt{3}} \cdot \dfrac{\sqrt{3}}{\sqrt{3}} \\[1.3 em] a &= 600 \sqrt{ 3 } \end{aligned} $$Step 2: Find hypotenuse c.
From the diagram above we can see that $ c = 2 \cdot a $. In this example we have:
$$ c = 2 \cdot 600 \sqrt{ 3 } = 1200 \sqrt{ 3 } $$