Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Assuming the average distance of the earth from the sun to be 149,700,000 km, and the angle subtended by the sun at the eye of a person on the earth to be 32’, find the sun’s diameter.

Answer

Let D km denote the diameter of the sun. Since the angle subtended by the sun is very small, therefore, its diameter is approximately equal to small arc of a circle with centre at the eye of the observer on the earth.

 ∴                     l = D,   r =  149,700,000 km
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Since straight theta space equals space l over r rightwards double arrow space fraction numerator 2 straight pi over denominator 15 space cross times space 45 end fraction space equals space fraction numerator straight D over denominator 149 comma space 700 comma space 000 end fraction
rightwards double arrow    straight D space equals space 2 over 675 space cross times space 22 over 7 space cross times space 149 comma 700 comma 000 space left parenthesis Approx. right parenthesis space equals space 1 comma 394 comma 000 space km space left parenthesis Approx right parenthesis.

Tips: -

Note:
1. The angle traced by hour hand in 1 hour is equal to open parentheses 360 over 12 close parentheses to the power of degree space space or space space 30 degree.
2. The angle traced by minute hand in 1 minute is equal to open parentheses 360 over 60 close parentheses to the power of ring operator space or space space 6 degree.

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