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masha68 [24]
2 years ago
15

A planet has a circular orbit around a star. It is a distance of 81,000,000 km from the centre of the star. It orbits at an aver

age speed of 46,000 km/h. How many Earth days does it take the planet to orbit the star? Give your answer to 2 sf.
Mathematics
1 answer:
slava [35]2 years ago
5 0

81,000,000 \text{ km} \left(\frac{1 \text{ h}}{46,000 \text{ km}} \right) =\frac{40500}{23} \text{ h} \\ \\ \frac{40500}{23} \text{ h} \left(\frac{1 \text{ days}}{24 \text{ hours}} \right) \approx \boxed{73 \text{ days}}

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8.4 in

Step-by-step explanation:

Solution:-

- We consider the large right angle triangle namely, " XVW "

- We will recall all the trigonometric ratios that are applicable to all right angled triangles.

- While we are dealing with trigonometric ratios we have the following terms that needs to be correlated with the given specific problem:

            Hypotenuse ( H ): Side opposite to 90 degrees angle

            Base (B): The side adjacent to the available angle ( θ )

            Perpendicular (P): The side opposite to the available angle ( θ )

- We will go ahead and mark our respective sides as follows:

            Angle ( θ ) : 34°

            Hypotenuse ( H ) : XW = 15 in

            Base ( B ) : VW

            Perpendicular ( P ) : VX

- Now recall all the trigonometric ratios studied:

           sin ( θ ) = P / H = VX / XW

           cos ( θ ) = B / H = VW / XW

           tan ( θ ) = P / B = VX / VW

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                             sin ( 34° ) = VX / 15

                             VX = 15*sin ( 34° )

                             VX = 8.387 .. ( 8.4 ) in

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3 years ago
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