Question

Find the values of x and y. Round your answers to the nearest tenth if necessary,

Answer 1

Answer:

$x=12,\\y=12\sqrt{3}$

Step-by-step explanation:

In any 30-60-90 triangle, the side lengths are in the ratio $x:x\sqrt{3}:2x$, where $2x$ is the hypotenuse, or longest side, of the triangle and $x$ is the side opposite to the 30 degree angle.

In the given 30-60-90 triangle, the longest side (hypotenuse) is marked as 24. Since $x$ is opposite to the 30 degree angle,

Therefore, we have:

$x=\frac{24}{2},\\x=\boxed{12}$

Based on our side length ratio $x:x\sqrt{3}:2x$, $y$ is then:

$y=x\sqrt{3}\text{ for}\implies x=12,\\y=\boxed{12\sqrt{3}}$

Answer 2

Answer:

$\huge\boxed{x=12;\ y=12\sqrt3\approx20.8}$

Step-by-step explanation:

Look at the picture.

We have:

$2a=24\\a=x\\a\sqrt3=y$

Therefore:

$x=24:2=12\\\\y=12\sqrt3\approx12\cdot1.73=20.76\approx20.8$