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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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Answer:

=−0.888168

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3 years ago
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alexdok [17]
Without using the trigonometry ratio, we can find the distance between the ship and the buoy by:

the distance between City and Lemont SUBTRACT the vertical distance between City and the point parallel to the Ship

The distance between the City and Lemont can be worked out using the Sin rule 
\frac{57.8}{sin(36)}= \frac{City-Lemont}{sin(92)}
City-Lemont= \frac{57.9sin(92)}{sin(36)} = 98.27.....≈98.3

The vertical distance between the City and the point parallel to the ship can be worked out using the Pythagoras theorem
\sqrt{57.8^{2}- 44.6^{2} } =36.765...≈36.8

The distance between the ship and the Buoy is given:
98.3-36.8=61.5 miles

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3 years ago
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Harman [31]
1. convert to improper fractions

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3 years ago
Need help pleasee!! :(
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