16. Given that the moon's mean angular diameter is 31' and that it is 24,000 miles away. Find its actual diameter to the nearest miles.

Solution

Note : The angle subtended by the actual diameter with the eye is called the "angular diameter".

Suppose AB is the actual diameter then Ð AOB = 31' is the angular diameter. Here O is the observer.

Now s = r q^c where AB = s, r = 24,000 miles.

17. Two cities 270 miles apart lie on the same meridian. Find their difference in latitude.

Solution

Here s = 270 miles. r = 3960 miles (of the earth)

18. A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 250 in a distance of 120 m. ?

Solution

19. A field is in the shape of a circular sector containing an angle p / 3 rad. Its straight sides are 100 feet each. What is its price per sq.foot if it is sold at the rate of $ 100 per foot of the frontage ?

Solution

Frontage mean length of the arc (s)
Here r = radius of the sector = 100 feet
and q = central angle = p / 3 rad

Index

1.1 Angles (Radians & Degrees)
1.2 Arc Length & Area of the circle
Supplementary Problems

Chapter 2