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andriy [413]
3 years ago
11

A right △ABC is inscribed in circle k(O, r). Find the radius of this circle if:

Mathematics
1 answer:
natta225 [31]3 years ago
8 0

We have been given that a right △ABC is inscribed in circle k(O, r).

m∠C = 90°, AC = 18 cm, m∠B = 30°. We are asked to find the radius of the circle.

First of all, we will draw a diagram that represent the given scenario.

We can see from the attached file that AB is diameter of circle O and it a hypotenuse of triangle ABC.

We will use sine to find side AB.

\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}

\text{sin}(30^{\circ})=\frac{AC}{AB}

\text{sin}(30^{\circ})=\frac{18}{AB}

AB=\frac{18}{\text{sin}(30^{\circ})}

AB=\frac{18}{0.5}

AB=36

Wee know that radius is half the diameter, so radius of given circle would be half of the 36 that is \frac{36}{2}=18.

Therefore, the radius of given circle would be 18 cm.

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