Question

One leg of a right triangle measures 6 inches. the remaining leg measures 6sqrt3 inches. what is the measure of the angle opposite the leg that is 6 inches long?

Answer 1

Answer:

The measure of the angle opposite the leg that is 6 inches long is

$30^{\circ}$

Step-by-step explanation:

We have been given sides of right triangle that is we will use pythagoras theorem:

$hypotenuse^2=side^2+side^2$

Here, we have one side which is 6 inches

And other side is $6\sqrt{3}$ inches on substituting the values in the formula above we get:

$hypotenuse^2=6^2+(6\sqrt{3})^2$

$hypotenuse^2=36+108$

$\Rightarrow hypotenuse^2=144$

$\Rightarrow hypotenuse=12$

The angle will be $sin\theta=\frac{perpendicular}{hypotenuse}$

$sin\theta=\frac{6}{12}$

$\Rightarrow sin\theta=\frac{1}{2}$

$\Rightarrow \theta=sin^{-1}(\frac{1}{2})$

$\Rightarrow \theta=30^{\circ}$

Hence,  the measure of the angle opposite the leg that is 6 inches long is

$30^{\circ}$

Answer 2

Hope this helps you.