Question

Express Y in terms of X

Answer 1

Answer:

$y=\sqrt{3x^2}$

Step-by-step explanation:

$In\ \triangle ABC\ three\ sides\ are\ equal\ so\ it\ is\ a\ equilateral\ triangle.\\\\All\ three\ angles\ will\ be\ of\ 60\textdegree.\\\\\angle ACB=60\textdegree\\\\\angle ACD=180-\angle ACB=180-60 =120\textdegree$

Cosine Formula: $AD^2=AC^2+CD^2-2\times AC\times CD\times \cos\angle ACD$

Use Cosine formula in $\triangle ACD$

$y^2=x^2+x^2-2\times x\times x\times \cos120\textdegree\\\\y^2=2x^2-2x^2(-\frac{1}{2})=2x^2+x^2\\\\y^2=3x^2\\\\y=\sqrt{3x^2}$