Question

Just don't understand these problems

Answer 1

Look at the pictures.

Method 1.

Use triangles from picture 1 and 2.

The triangleABC is isosceles triangle. Therefore
`|AB| = |BC| = 6`.

`|AC|=6\sqrt2=(x\sqrt3)/(2)\\\\(x\sqrt3)/(2)=6\sqrt2\ \ \ |\cdot2\\\\x\sqrt3=12\sqrt2\ \ \ |\cdot\sqrt3\\\\3x=12\sqrt6\ \ \ |:3\\\\x=4\sqrt6`

Answer: C. 4√6

Method 2

Use the trigonometric functions:

`\sin45^o=(6)/(|AC|)\ \ \ /\sin45^o=(\sqrt2)/(2)/\\\\(6)/(|AC|)=(\sqrt2)/(2)\ \ \ |cross\ multiply\\\\|AC|\sqrt2=2\cdot6\ \ \ |\cdot\sqrt2\\\\2|AC|=12\sqrt2\ \ \ |:2\\\\|AC|=6\sqrt2`

`\sin60^o=(6\sqrt2)/(x)\ \ \ /\sin60^o=(\sqrt3)/(2)/\\\\(6\sqrt2)/(x)=(\sqrt3)/(2)\ \ \ |cross\ multiply\\\\x\sqrt3=6\sqrt2\cdot2\ \ \ \ |\cdot\sqrt3\\\\3x=12\sqrt6\ \ \ \ |:3\\\\x=4\sqrt6`