Question

what is the length of u and v in this 30 - 60 - 90 triangle? u = 4√2 v = 8 u = 16 v = 8 u = 8 v = 4√3 u = 4√3 v = 8

Explanation:

Step1: Recall 30 - 60 - 90 triangle side ratios

In a 30 - 60 - 90 triangle, if the side opposite the 30° angle is \(a\), the side opposite the 60° angle is \(a\sqrt{3}\), and the hypotenuse is \(2a\). Here, the side opposite 30° is 4.

Step2: Find the hypotenuse \(v\)

Since the hypotenuse \(v = 2a\) (where \(a = 4\)), then \(v=2\times4 = 8\).

Step3: Find the side \(u\) (opposite 60°)

Since the side opposite 60° is \(a\sqrt{3}\) (where \(a = 4\)), then \(u = 4\sqrt{3}\).

Answer:

\(u = 4\sqrt{3},v = 8\) (the fourth option)