Question

What is the answer lol somebody help me please and thank you !

Answer 1

I'm guessing that you know about 45-45-90 and 30-60-90 triangles.

In 45-45-90 triangles, the legs are in a ratio such that the hypotenuse is $\sqrt{2}$ times the legs.

In 30-60-90 triangles, the legs are in a ratio of 1:$\sqrt{3}$:2

In the picture given we have been given a value of the side of the 45-45-90 triangle. We can deduce that the value of the hypotenuse is 9$\sqrt{2}$ because of the ratio of the sides of a 45-45-90 triangle.

The 30-60-90 triangle shares the same hypotenuse, and so we now know a value of one of its sides as well. The ratio of the side of value 'x' and the hypotenuse is $\sqrt{3}$ : 2

We can create an equation to solve for x using these ratios:

$\frac{\sqrt{3} }{2}$ = $\frac{x}{9\sqrt{2} }$

Cross multiply:

2x = 9$\sqrt{6}$

x = $\frac{9\sqrt{6} }{2}$

Option C