Use similar triangles to find

Question

Answer 1

In the above triangle, we know that two of the angles are 30 and 90 degrees. Because the sum of the degrees of all three angles in a triangle is 180 degrees, the unknown angle is 180-90-30= 60 degrees. We now know we have a 30-60-90 triangle with the shorter leg (opposite the 30 degree angle) having a length of 6. The hypotenuse is twice the length of the short leg, which would be 12. Finally, the longer leg is the square root of three times the small leg. Therefore the longer leg is 6*square root of 3

Answer 2

This is a 30-60-90 right triangle. All triangles with that description have the following properties.

1. The hypotenuse is always twice the short leg (the short leg is opposite the 30 degree angle).
2. The long leg (opposite the 60 degree angle) is always √3 times the short leg.

In this particular case the short leg measure is given as 6.

That means the hypotenuse (x) is 2 times 6 or 12.

Also the long leg (w) must be 6√3.

This Desmos graph gives some details on "why" the above is true:

desmos.com/calculator/7e6amnwol9