TRIGONOMETRY

PROBLEM SOLVING

DIRECTIONS: SOLVE THE FOLLOWING PROBLEMS

1.) From an observation post 330 ft from the base of a building, the angles of elevation of the top and

bottom of a flagpole situated on top of the building are 63O20’ and 53O40’. Find the height of the flagpole.

2.) From an airplane at an altitude of 1200 m, the angle of depression of a rock on the ground measures 28 O. Find the distance from the plane to the rock.

3.) From a height of 38 m above sea level, two ships are sighted due west. The angles of depression are 53 O

and 28O. How far apart are the ships?

4.) A 100 m look – out tower is built on a high hill above the most of the surrounding land. If a ranger in the tower sights a fire at an angle of 15O from the horizontal, how far is the fire from the base of the tower?

5.) As you walk on a straight level path toward a mountain, the measure of the angle of elevation to the peak from one point is 33O. From a point 1000 ft closer, the angle of elevation is 35O. How high is the mountain?

6.) A child holds the end of a kite string 36 in. above the ground. The string is taut and it makes a 68 O angle with the horizontal. How high off the ground is the kite if 540 in. of strong are out?

7.) A jet took off at a rate of 260ft/s and climbed in a straight path for 3.2 min. What was the angle of elevation of its path if its final altitude was 12,000 ft?

8.) The extension ladder on top of a 6.0 – ft high hook and ladder truck is 150 ft long. If the angle of elevation of the ladder is 70O, to what height on a building will the ladder reach?

9.) The world’s longest escalator is at the Leningrad Underground in Lenin Square. The escalator has an angle of elevation of 10.36O and a vertical rise of 195.8 ft. Find the length of the escalator.

10.) A television antenna stands on the edge of the top of a 52 – story building. From a point 320 ft from the base of the building, the angle of elevation to the top of the antenna is 64 O. If each story is 12 ft high, find the height of the antenna.

11.) Suppose that 30 milligrams of a radioactive substance decrease to 10 milligrams after 5 years. Find the half – life of the substance.

12.) An Egyptian mummy is found to contain 75% of its Carbon 14. If the half – life of Carbon 14 is approximately 5750 years, how old is the mummy?

13.) The growth rate for a particular bacterial culture can be calculated using the formula B=900 (2 )t50 ,

where B is the number of bacteria and t is the elapsed time in hours.

a.) How many bacteria will be present after 5 hours?

b.) Approximately how many hours will it take for there to be 9000 bacteria present in the culture?

c.) How many hours will it take for there to be 30,000 bacteria present in the culture?

14.) In the town of Middlebury, the spread of a virus was such that t weeks after its outbreak, f(t) persons had

contracted it, where f ( t )= 12,000

1+599e−0.7 t.

a.) How many people had the virus at its break?

b.) How many weeks will it take for 3000 people to contract the virus?

c.) How many weeks will it take for 7000 people to contract the virus?

15.) As a person’s experience increases, competence at completing a task increases rapidly at first, and then slows down as additional experience is gained. This phenomenon can be represented by a learning curve.

After t hours of typing, Jose can type of f ( t )=80 (1−e−0.025 t ) words per minute.

a.) How many words per minute can he be expected to type after 10 hours of practice?

b.) How many words per minute can Jose type after 25 hours of practice?

16.) Two ships leave the same port at 7am. The first ship sails towards Europe on a 54O course at a constant rate of 36 mi/hr. The second ship, with a tropical destination, sails on a 144O course at a constant speed of 42mi/hr. Find the distance between the ships at 11am.

17.) A jet flew 140 miles on a course of 196O and then 120 miles on a course of 106O. Then the jet returned to its starting point via the shortest route possible. Find the total distance that the jet traveled.

18.) A pilot of San Antonio – to – Houston express plane traveling on a course of 79O sights the Austin airport. His line of sight forms a right angle with the plane’s line of travel. Find the bearing of the Austin port.

19.) The bearing of a buoy from a ship 8.7 miles away is 64O. The ship is headed due north, and the navigator plans to change course when the buoy has a bearing of 154O. How much farther will the ship travel before the change of course is needed?

20.) The navigator of a ship on a 44O course sights a buoy with bearing 134O. After the ship sails 15 km along the same course, the navigator sights the same buoy with bearing 168O. Find the distance between the ship and the buoy at the time of each sighting.