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# Trigonometry Word Problems : Radius and Circumference of the Earth

1 The engine of a sport car rotates at 5,000 revolutions per minute (rpm). Calculate the angular speed of the engine in radians per second.

2 We will redo Eratosthenes's famous calculations of the measurements of the Earth that he made in 236 BC. There are two cities on the surface of the Earth that are 1,702.0 miles apart. If the difference between the angles created by the shadows is 25 degrees

a) What is the radius of the Earth (assume a perfect sphere)
b) What is the circumference of the Earth (once again assuming a perfect sphere)
c) Not assuming the perfect sphere, what is the "true" circumference of the Earth and compare it to the value you calculated.
d) What is the percent difference?
e) What are some possible causes of the difference?

3 Classify the Given angle:

177 degrees a) Acute, b)Right , C) Obtuse, d) Straight

4- a)Convert 18 degrees to radians

b) convert -4&#61552; to degrees.

c) which angle below is co-terminal to 415?
1) 85 degrees
2) -85 degrees
3) -55 degrees
4) 55 degrees

5- Find the lengh of the arc on a circle of radius r= 16 inchesby a central angle &#61553; = 60 degrees. A) 20 inches, b) 1.5 inches c) 16.76 inches d) 100 inches.

#### Solution Preview

Dear Student:

Please see the MSWord File attached too..
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1 The engine of a sport car rotates at 5,000 revolutions per minute (rpm). Calculate the angular speed of the engine in radians per second.