Question

What is X in the simplest radical form and what is the measure of angle A?

Answer 1

ANSWER

• x = 9√5

,

• m∠A = 30º

EXPLANATION

By the intersecting chords theorem, we know that if one of the chords passes through the center and the chords are perpendicular, then:

$AH=x$

We can find AH using the pythagorean theorem, because SAH is a right triangle:

$\begin{gathered} AH^2=9^2+18^2 \\ AH=\sqrt[]{81+324} \\ AH=9\sqrt[]{5} \end{gathered}$

Therefore x = 5 too.

Then, since SAH is a right triangle, we can use the sine of angle A to find its measure:

$\begin{gathered} \sin A=\frac{9}{18} \\ \sin A=\frac{1}{2} \\ A=\sin ^{-1}\frac{1}{2} \\ A=30º \end{gathered}$