Question

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

Explanation:

Step1: Recall 30 - 60 - 90 triangle ratios

In a 30 - 60 - 90 triangle, if the short leg is \(x\), the long leg is \(x\sqrt{3}\), and the hypotenuse is \(2x\).

Step2: Relate long leg to hypotenuse

Let the long leg \(l=x\sqrt{3}\), and hypotenuse \(h = 2x\). From \(l=x\sqrt{3}\), we get \(x=\frac{l}{\sqrt{3}}\). Then \(h = 2\times\frac{l}{\sqrt{3}}\). If the long leg \(l = 8\), we first divide 8 by \(\sqrt{3}\) (to get \(x\)) and then multiply by 2 (to get hypotenuse).

Answer:

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