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Trigonometry, Area, Volume and Word Problems - MTH212 Unit 4

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1. Along a straight shoreline, two lighthouses, A and B, are located 2000 feet apart. A buoy lies in view of both lighthouses, with angles 1, 2, and 3 as indicated. (Angle 1 is denoted by , angle 2 is denoted by , and angle 3 is denoted by .)

A. By looking at the picture, do you think is an acute, obtuse, right, or a straight angle?

B. What can you say about the relationship between and ?

C. If , what is the measurement for ? Show all work as to how you received your final answer.

2. The two parallel lines a and b are cut by a transversal c. Find the missing angles, and give a brief explanation as to how you found each one.

3. A rectangle is a parallelogram with four right angles. A rectangle has a width of 15 feet and a diagonal of a length 22 feet; how long is the rectangle? What is the perimeter of the rectangle? Round to the nearest foot. Show all work to receive full credit.

Length of rectangle:

Perimeter of the rectangle:

4. The following picture shows a high school gymnasium. The art class is planning to create a circular design for the center of the floor, and the students know the diameter of the circle must be 16 feet. They have a budget of $100 and want to make sure they have enough money to buy paint to cover the full circle.

A. What is the area of the circle that needs to be painted?

B. If a pint of paint covers 60 ft2, how many pints of paint are needed to complete the job? Round up to the nearest pint.

C. If each pint costs $6.95, find the cost of the paint needed.

D. Will the art class be able to make its budget?

5. Judy and Pete are building a new house and want to carpet their living room, except for the entranceway and the semicircle in front of the fireplace that they want to tile (Alexander & Koeberlein, 2003).

A. How many whole square yards of carpeting are needed? (Hint: There are 9 square feet in one square yard.) Only whole square yards of carpet are sold. Show all work to receive full credit.

A. How many square feet are to be tiled? Show all work to receive full credit.

6. An observatory has the shape of a right circular cylinder topped by a hemisphere. The radius of the cylinder is 10 ft and its altitude measures 24 ft (Alexander & Koeberlein, 2003).

A. What is the approximate surface area of the observatory? Round to the nearest foot.
Show all work to receive full credit. (Hint: Remember the top and bottom of the cylinder will not be painted, so do not include them in your surface area. However, note that the hemispherical dome will be painted.)

B. If 1 gallon of paint covers 300 ft2, how many gallons are needed to paint the surface if it requires three coats? Round up to the nearest gallon. Show all work to receive full credit.

7. Two angles are supplementary of each other. Twice one angle is equal to the other
angle minus the product of six and eight.

A. Set up a system of linear equations to represent the two angles. (Hint: You will need two equations and two unknowns.)

B. Graph each of the equations on one rectangular coordinate system. (Hint: You must get y by itself before graphing.) Scale the graph accordingly; you will need your x-axis and y-axis to go to at least 200.

C. What do you notice about the intersection of the two lines?

D. Solve the system of equations in part A to determine the degrees of each angle by using Gaussian elimination.


Alexander, D. C., & Koeberlein, M. G. (2003). Elementary geometry for college students (3rd ed.). Boston: Houghton Mifflin.
MTH 212

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