Question

question 9 of 10 which of the following could be the ratio between the lengths of the two legs of a 30 - 60 - 90 triangle? check all that apply. a. 1 : $sqrt{3}$ b. $sqrt{3}:sqrt{3}$ c. $sqrt{3}:3$ d. 1 : $sqrt{2}$ e. $sqrt{2}:sqrt{2}$ f. $sqrt{2}:sqrt{3}$

Explanation:

Step1: Recall side - length ratio of 30 - 60 - 90 triangle

In a 30 - 60 - 90 triangle, if the shorter leg (opposite the 30 - degree angle) has length \(a\), the longer leg (opposite the 60 - degree angle) has length \(a\sqrt{3}\), and the hypotenuse has length \(2a\). The ratio of the shorter leg to the longer leg is \(a:a\sqrt{3}=1:\sqrt{3}\), and the ratio of the longer leg to the shorter leg is \(\sqrt{3}:1\). Also, \(\sqrt{3}:3=\frac{\sqrt{3}}{3}=\frac{1}{\sqrt{3}}\), which is equivalent to \(1:\sqrt{3}\) when inverted.

Answer:

A. \(1:\sqrt{3}\), C. \(\sqrt{3}:3\)