 Hello friends, we are going to discuss yet another problem and this problem It says assuming the average distance of the earth from the Sun to be 925 0000 miles and Angles obtained by the Sun at the eye of a person on the earth to be 32 minutes So you have to find out the Sun's diameter. So probably this could be one way of finding Sun's diameter if at all we know How far the Sun is on an average from the earth now they have you they are using a term average over here average distance average distance because you know that earth's orbit around the Sun is not a Circle its ellipse so hence the distance between the earth and Sun keeps on Changing so hence they have taken an average value Now how to solve this problem? So here in this problem. There is a basic assumption the basic assumption is since theta is very very small That is this is 32 degrees. Sorry 32 minutes So we can assume that the diameter which is subtending this theta on the eye of the observer We can assume that this diameter is almost equivalent to an arc whose Ark of a circle whose center is at the eye of the observer Okay, and the radius is nothing but the distance between average distance between the Sun and the earth Now, let us say how to solve this problem so theta is 32 minutes, so we have to first convert it into radiance because All the operations are all the formula whichever we have learned We have to use radiance in and for measuring theta So angle is 32 minutes, so that is nothing but 32 upon 60 degrees. Why because one minute or 60 degrees Sorry 60 minutes is equal to 1 degree Okay, so hence, you know that one minute will be 1 upon 60 Degrees so hence 32 minutes will be 32 upon 60 degrees and we also know that Pi radian is equivalent to or is equal to 180 degrees So hence, I know that one degree will be equal to pi upon 180 radians Isn't it? So when once I know this so hence The angle after conversion you will get 2 pi by 365 radians This is the angle subtended by the diameter of the Sun Onto the eye of the observer now It's also given that distance between Sun and Earth is 9 to 5 triple zero double zero miles Since theta is very small. I have written the assumption diameter D Can we assume to be a small arc of a circle centered at observer's eye? radius of which is L radius of what radius of the Circle of which we are saying D is in small arc Now, we know that angle subtended by an arc is nothing but arc length our client divided by The radius of the circle so angle subtended by the center is nothing but arc length divided by the radius That's what we have written theta is equal to D by L So by cross multiplication you can get D is equal to L theta, right? So value of L was given value of theta was given in our relevant unit so hence if you see this is in miles and this is in Radians so hence we find out that the diameter is approximately These many miles. This is how You can find out or a you know approximately find out the diameter of Sun So what is the learning learning is here? We have used one formula. What is that formula formula is theta is equal to? L upon R where L is the arc length arc length and Radius is sorry R is radius of the circle Radius of the circle, right? So this is what the drawing would look like. So let us say this is the arc and This is the sector. Let us say this is theta. This is L and this is R So theta in radians is given by L upon Our mind you theta has to be in radian is in radians Okay, and other assumption we used what was the assumption since theta is too small That means the diameter can be assumed to be Part of an circle that is an arc whose radius is nothing but the distance between Earth and the Sun so that assumption with this formula we used to solve this problem. Thank you