Trigonometry Applications to Word Problems

You have been contacting cartographers and land surveyors to explore how they utilize graphs of functions in their work , and have learned that they create formulas to calculate size and mass. Complete the following problems:

1. A lobster boat is situated due west of a lighthouse. A barge is 12 km south of the lobster boat . From the barge the bearing to the lighthouse is 63 degrees ( 12 km is the length of the side adjacent to the 63 degree bearing ). How far is the lobster boat from the light house?

2. A recent land survey was conducted on a vacant lot where a commercial building is to be erected. The plans for the future building construction call for a building having a roof supported by two sets of beams. The beams in the front are 8 feet high and the back beams are 6.5 feet high. The distance between the front and back beams is feet. At what angle will the roof lay on the front beam?

3. Latitude presents special mathematical considerations for cartographers. Latitude is the north-south location on the earth between the equator and the poles. Since the earth flattens slightly at the poles, a nautical mile varies with latitude. A nautical mile is given by N (e) = 6066 -31 * cosine 2e. e represents the latitude in degrees.
- What is the length of a British nautical mile at Chicago (latitude of 42 degrees)?
- What is the length of a British nautical mile at the North Pole (latitude of 90 degrees)?
- Express N(e) in terms of cosine e only, do not use the double angle.
- At what latitude north is the length of a British nautical mile found to be 6040 feet?

4. A guy wire (a type of support used for example, on radio antennas) is attached to the top of a 50 foot pole and stretched to a point that is d feet from the bottom of the pole. Express the angle of inclination as a function of d.