There's a doubt that i have in trigonometric functions. (class 11 - maths)
Question -
The moon's distance from the earth is 360000km and its diameter subtends an angle of 31 minutes at the eye of the observer. Find the diameter of the moon.
tan(31min)=radius/distance
31min can be converted to radian and is a small angle.
tan(small angle in radian)=angle itself nearly
angle in radian=radius/distance
Radius hence dia. can now be found.
We can see here that the angle subtended at the eye is 31 minutes or (31/60) degree.
this can also be written as (31/60 * 22/7 * 1/180) radians.
so now we know that x(in radian) = length of arc/ radius, here radius can be taken as 360000 km
and the arc can be taken as the diameter of moon because the length of both will be approximately the same
so we get the equation as diameter of moon = (31/60 * 22/7 * 1/180 * 360000) km or (0.516 * 3.14 * 2000) km
or 3240.48 km.