Question

Find the missing side length leave your answers as radicals in the simplest form.

Answer 1

Answer:

Part 1) $x=\frac{10\sqrt{3}}{3}\ units$

Part 2) $y=5\ units$

Step-by-step explanation:

step 1

Find the value of x

In the right triangle of the figure

$sin(30^o)=\frac{(5\sqrt{3}/3)}{x}$ ---> opposite side angle of 30 degrees divided by the hypotenuse

Remember that

$sin(30^o)=\frac{1}{2}$

substitute

$\frac{1}{2}=\frac{(5\sqrt{3}/3)}{x}$

solve for x

$x=\frac{5\sqrt{3}}{3}(2)$

$x=\frac{10\sqrt{3}}{3}\ units$

step 2

Find the value of y

In the right triangle of the figure

$cos(30^o)=\frac{y}{x}$ ---> adjacent side angle of 30 degrees divided by the hypotenuse

we have

$x=\frac{10\sqrt{3}}{3}\ units$

$cos(30^o)=\frac{\sqrt{3}}{2}$

substitute

$\frac{\sqrt{3}}{2}=\frac{y}{\frac{10\sqrt{3}}{3}}$    

$y=(\frac{\sqrt{3}}{2})(\frac{10\sqrt{3}}{3})$

$y=5\ units$