Question

In the figure above, $△ABC$ is similar to $△XYZ$. Find the value of $\cos A$.

• A. $\frac{1}{2}$
• B. $\frac{\sqrt{3}}{2}$
• C. $\sqrt{3}$
• D. $2$

Answer 1

The correct option is B $\frac{\sqrt{3}}{2}$

Since the triangles are similar according to the sequence, $\Delta ABC\Delta XYZ$

The angles would thus be congruent, yielding $\angle X=\angle A$

$\therefore \cos A=\cos X=\frac{\sqrt{(4{)}^2-(2{)}^2}}{4}=\frac{\sqrt{12}}{4}=\frac{\sqrt{3}}{2}$