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Six Geometry Word Problems

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The finished product should be one combined document for the entire group, showing all calculations and graphical representations used.

1. Find the length L from point A to the top of the pole.

2. Lookout station A is 15 km west of station B. The bearing from A to a fire directly south of B is S 37°50' E. How far is the fire from B?

3. The wheels of a car have a 24-in. diameter. When the car is being driven so that the wheels make 10 revolutions per second, how far with the car travel in one minute?

4. A regular octagon is inscribed in a circle of radius 15.8 cm. Find the perimeter of the octagon.

5. What is the angle of elevation of the sun when a 35-ft mast casts a 20-ft shadow?

6. Two distinct, nonparallel lines are tangent to a circle. See picture below. The measurement of the angle between the two lines is 54° (angle QVP).

Suppose the diameter of the circle is 2cm. What is the distance VP?
Suppose the distance VP is 3.93 cm. What is the diameter of the circle?
Find a formula for d, the diameter of the circle, in terms of VP.
Find a formula for VP in terms of d, the diameter of the circle.

See attached file for full problem description.

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