Question

From the earth, the moon subtends an angle of approximately 0.5°. If the distance to the moon is approximately 240,000 miles, find an approximation for the diameter of the moon accurate to the nearest hundred miles.

Answer 1

The subtended angle and by an arc is given by:
S = r∅
Although the arc is circular, the huge amount of distance means that it is almost equivalent to the director.
D = 240,000 x (0.5 x π)/180
D = 2094 miles

Answer 2

The approximation for the diameter of the moon accurate to the nearest hundred miles is s =  +- 2100 miles

Further explanation

Arc Measure definition is,  in a circle, arc degree measure is equal to the measure of the central angle that intercepts the arc. Whereas the arc Length definition is, In a circle, the length of an arc is a portion of the circumference. Where the letter "s" is used to represent arc length.      

$s = r * \theta$ (Radian Measure and Arc of a Circle).

There is a formula which relates the arc length of a circle of radius, r, to the central angle, θ in radians.

The radian measure θ of a central angle is defined as the ratio of the length of the arc  the angle subtends s, divided by the radius of the circle r.

where s = the arc length

$\theta$ = angle  in radians

$0.5 degrees *  \frac{\pi}{180}  = 0.008726646 radians \\ r = 240000 miles  \\ s  = 240000 * 0.008726646$

$s = 2094.4 miles$ or

$s =  +- 2100 miles$

So the approximation for the diameter of the moon accurate to the nearest hundred miles is s =  +- 2100 miles

Learn more

1. Learn more about the radian measure of the angle https://brainly.com/question/4675968

Answer details

Grade:  9

Subject:  physics

Chapter:  the radian measure of the angle

Keywords:  moon