Question:
assuming average distance of the earth from the sun to be 149700000km 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:
Given θ = 32 minutes = (32/60)° = (32/60)*(π/180)
and r = 149700000 km
Now, θ = arc/radius
=> (32/60)*(π/180) = d/149700000
=> d = 149700000 * (32/60)*(π/180)
=> d = (149700000 * 32 *π)/(60 * 180)
=> d = {149700000 * 32 * (22/7)}/(60 * 180)
=> d = (149700000 * 32 * 22)/(7 * 60 * 180)
=> d = (1497000 * 32 * 22)/(7 * 6 * 18)
=> d = (1497000 * 32 * 11)/(7 * 3 * 18) {22 and 6 are divided by 2}
=> d = (1497000 * 16 * 11)/(7 * 3 * 9) {32 and 18 are divided by 2}
=> d = (263472 * 1000)/189
=> d = 1394.031746 * 1000
=> d = 1394031.746 km
So, the diameter of the sun is 1394031.746 km
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