Question

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

Answer 1

• x = 9√5

,

• m∠A = 30º

Step-by-step 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=(9)/(18) \\ \sin A=(1)/(2) \\ A=\sin ^(-1)(1)/(2) \\ A=30º \end{gathered}`