Question

Find the missing lengths in the triangle. round to the nearest tenth if necessary

Answer 1

Answer:

$x=8,\\y\approx 6.9$

Step-by-step explanation:

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

In the given diagram, the side labelled 4 is opposite to the 30 degree angle. Since $x$ is labelled as the hypotenuse of the triangle, $x$ must be $4\cdot 2=\boxed{8}$.

Variable $y$ must then represent $x\sqrt{3}$ for $x=4$, yielding $y=4\sqrt{3}\approx \boxed{6.9}$