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

What is X in the simplest radical form and what is the measure of angle A?-example-1
User Adis
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1 Answer

6 votes

ANSWER

• 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}

User Lubiluk
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