Question

i have been given the long leg in this 30 - 60 - 90 triangle. how do i find the hypotenuse? divide 8 by \sqrt{3} divide 8 by \sqrt{3}, then multiply that answer by 2 divide 8 by 2 divide 8 by 2, then multiply that answer by \sqrt{2}

Explanation:

Step1: Recall 30 - 60 - 90 triangle side ratios

In a 30 - 60 - 90 triangle, if the short leg (opposite 30°) is \(a\), the long leg (opposite 60°) is \(a\sqrt{3}\), and the hypotenuse is \(2a\).
If the long leg \(l=a\sqrt{3}\), then \(a = \frac{l}{\sqrt{3}}\).

Step2: Find the hypotenuse

The hypotenuse \(h = 2a\). Substituting \(a=\frac{l}{\sqrt{3}}\) (where \(l\) is the long leg), we get \(h=\frac{2l}{\sqrt{3}}\). If \(l = 8\), first divide 8 by \(\sqrt{3}\) to get \(a=\frac{8}{\sqrt{3}}\), then multiply by 2 to get the hypotenuse.

Answer:

Divide 8 by \(\sqrt{3}\), then multiply that answer by 2.