Question

Question 13 of 28Which of the following represents the ratio of the long leg to the short leg inthe right triangle shown below?30O A. 1:4√3OB. √3:1O C. 1:2O D. 2:160°

Answer 1

Solution:

Given a right triangle;

Where the long leg, x, is, the side opposite the angle 60°

And the short leg, y, is the side opposite angle 30°

To find the ratio of the long leg to short leg,

$\begin{gathered} For\text{ long leg} \\ \sin\theta=\frac{Opposite}{Hypotenuse} \\ Where \\ \theta=60\degree \\ \sin60\degree=\frac{x}{Hypotenuse} \\ \frac{\sqrt{3}}{2}=\frac{x}{Hypotenuse} \\ Hypotenuse=\frac{2x}{\sqrt{3}} \end{gathered}$

For the short leg

$\begin{gathered} \cos\theta=\frac{Adjacent}{Hypotenuse} \\ \theta=60\degree \\ \cos60\degree=\frac{y}{Hypotenuse} \\ Where \\ \cos60\degree=\frac{1}{2} \\ \frac{1}{2}=\frac{y}{Hypotenuse} \\ Hypotenuse=2y \end{gathered}$

The ratio of the long and short leg will be

$\begin{gathered} \frac{2x}{\sqrt{3}}=2y \\ \frac{2x}{2y}=\frac{\sqrt{3}}{1} \\ \frac{x}{y}=\frac{\sqrt{3}}{1} \\ x:y=\sqrt{3}:1 \end{gathered}$

Hence, the answer is B.