The towns A and B are on the circle of latitude 24 degrees N.The longitude of A is 108degrees E and longitude B is 75 degrees E.
a. Calculate the radius of the circle of latitude 24 degrees N.
b.The shortest distance between A and B measured along the circle of latitude 24 degrees N. Pi =22/7 r=6300
To answer these questions, we need to use some basic facts about circles and spherical geometry. Here's how you can calculate the radius of the circle of latitude 24 degrees N and the shortest distance between towns A and B along this circle:
a. Calculate the radius of the circle of latitude 24 degrees N:
To calculate the radius, we can use the formula:
Radius = (Earth's circumference at the equator) * (cos(latitude))
First, we need to find the circumference of the circle at the equator. The Earth's equatorial circumference is approximately 40,075 kilometers.
So, the radius of the circle of latitude 24 degrees N can be calculated as:
Radius = 40,075 km * cos(24)
We substitute the cosine of 24 degrees into the formula and calculate the result.
b. Calculate the shortest distance between A and B measured along the circle of latitude 24 degrees N:
To calculate the shortest distance, we use the formula:
Distance = (angle subtended at the center of the circle) * (radius of the circle)
First, we need to find the angle subtended at the center of the circle by towns A and B. This can be calculated as the difference in longitudes between A and B, multiplied by the circumference of the circle and divided by 360 degrees.
Angle = |longitude_A - longitude_B| * (circumference of the circle) / 360
We substitute the longitudes of A and B into the formula and calculate the result. Then we calculate the shortest distance by multiplying the angle by the radius of the circle.
Distance = Angle * Radius
Remember to use the given value of π (pi) and the given radius (r) in the final calculation.