Math

Question1. Earth’s radius is 6371 km6371 \mathrm{~km}. Distance Dhaka to Delhi is 1882 km1882 \mathrm{~km}. Find the angle at Earth's center.
2. Cyclist travels from A to B at 250 m/min, with an angle of 151^{\circ} 5^{\prime} at Earth's center (6440 km6440 \mathrm{~km} radius). Time taken in hours?
3. Circle radius is 35 m. An arc subtends angle π4\frac{\pi}{4} at the center. Find the arc length.

Studdy Solution

STEP 1

Assumptions1. The radius of the earth is6371 km. The distance between Dhaka and Delhi is188 km3. The distance between two points on the surface of a sphere can be treated as the arc length of a circle with the sphere's radius

STEP 2

We can use the formula for the arc length of a circle to find the angle. The formula isArclength=RadiustimesAngleArc\, length = Radius \\times AngleWhere the angle is in radians.

STEP 3

We can rearrange the formula to solve for the angle.
Angle=ArclengthRadiusAngle = \frac{Arc\, length}{Radius}

STEP 4

Now, plug in the given values for the arc length (the distance between Dhaka and Delhi) and the radius (the radius of the earth) to calculate the angle in radians.
Angle=18826371Angle = \frac{1882}{6371}

STEP 5

Calculate the angle in radians.
Angle=18826371=0.295radiansAngle = \frac{1882}{6371} =0.295\, radians

STEP 6

To convert the angle from radians to degrees, we can use the conversion factor 180π\frac{180}{\pi}.
Angleindegrees=Angleinradianstimes180πAngle\, in\, degrees = Angle\, in\, radians \\times \frac{180}{\pi}

STEP 7

Plug in the value for the angle in radians to calculate the angle in degrees.
Angleindegrees=0.295times180πAngle\, in\, degrees =0.295 \\times \frac{180}{\pi}

STEP 8

Calculate the angle in degrees.
Angleindegrees=0.295times180π=16.degreesAngle\, in\, degrees =0.295 \\times \frac{180}{\pi} =16.\, degreesThe degree of angle Dhaka and Delhi would make at the center of the earth is approximately16. degrees.

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