Precalculus
Name:
Unit 4 - Trigonometry
Date:
Thursday January 23, 2014
Homework More Applications with Bearing and Angles of Elevation/Depression
Remember to follow all the steps and communicate your process clearly.
1.) Draw a diagram.
Don’t be afraid to make it large. Draw triangles that look like right triangles.
2.) Label the diagram appropriately.
The better your diagram is labeled, the better you will be able to communicate your thought process. Remember there are more variables than
just x available to be used to label an unknown side length or angle. Similarly, you should not use x to represent more than one item in a problem.
3.) Set up an equation or equations in terms of trigonometric functions.
4.) Solve the equation(s). Consider whether your calculations seem reasonable.
5.) Answer the original question using correct units.
1.
A straight trail leads from the Alpine Hotel, elevation 8000 feet, to a scenic overlook, elevation 11,100 feet.
The length of the trail is 14,100 feet. What is the inclination (grade) of the trail? (i.e Find the angle of
elevation from the base of the hotel.)
2.
Meteorologists find the height of a cloud using an instrument called a ceilometer. A ceilometers consists of a
light projector that directs a vertical light beam up to the cloud base and a light detector that scans the cloud to
detect the light beam. On December 1, 2003, at Midway Airport in Chicago, a ceilometer is set up with a
base distance of 300 feet between the light projector and the light detector in order to find the height of the
cloud cover. If the angle of elevation of the light detector is 75, what is the height of the cloud cover?
Round your answer to the nearest foot.
3.
A ship is just offshore of New York City. A sighting is taken of the Statue of Liberty, which is about 305 feet
tall. If the angle of elevation to the top of the statue is 20, how far is the ship from the base of the statue?
Give your answer in feet and inches.
4.
A security camera in a neighborhood bank is mounted on a wall 9 feet above the floor. What angle of
depression should be used if the camera is to be directed to a spot 6 feet above the floor and a12 feet from the
wall?
5.
Adorning the top of the Board of Trade building in Chicago is a statue of Ceres, the Roman goddess of wheat.
From street level, two observations are taken 400 feet from the center of the building. The angle of elevation
to the base of the statue is found to be 55.1; the angle of elevation to the top of the statue is 56.5. What is
the height of the statue? Give your answer in feet and inches.
6.
A blimp suspended in the air at a height of 500 feet, lies directly over a line from Soldier Field to the Adler
Planetarium near Lake Michigan. The blimp is between the two locations. If the angle of depression from the
blimp to the stadium is 32 and from the blimp to the planetarium is 23, find the distance between Soldier
Field and the Adler Planetarium. Round your answer to the nearest hundredth of a mile. (5280 feet = 1 mile)
7.
A Boeing 777 aircraft takes off from O’Hare Airport on runway 2 LEFT which has a bearing of N20E. After
flying for one mile, the pilot of the aircraft requests permission to turn 90 and head toward the northwest.
The request is granted. After the plane goes 2 miles in this direction, what bearing should the control tower
use to locate the aircraft?