Download Word Problem Applications

Algebra & Analytic Geometry
Unit 6 – Trigonometry
Name & Date
WORD PROBLEM APPLICATIONS
1) How do you think the length of a shadow of a 30 foot tree will change over the course of a sunny day?
Answer the following questions to determine if your hypothesis is correct.
A) Find the length of the shadow when the angle of elevation of the sun is 250 up from the horizon.
B) Find the length of the shadow when the angle of elevation of the sun is 700 up from the horizon.
C) Find the angle of elevation of the sun if the shadow is 23 feet long.
Angle of Elevation is the angle formed by a horizontal line
and a line of sight to a point above the line.
Angle of Depression is the angle formed by a horizontal line
and a line of sight to a point below the line.
**Since horizontal lines are parallel, the angle of elevation
will be congruent to the angle of depression because
of the
.
2) Gertie the gopher is looking at a tree that is 100 feet away from her nest. If the angle of elevation between
Gertie’s nest and the top of the tree is 23°, how tall is the tree?
3) A soldier in a 75 foot tower spots a fellow soldier’s vehicle approaching in the distance. The soldier in the
tower spots the vehicle at an angle of depression of 8o. From the ground, how far is the vehicle from the tower
(the horizontal distance)?
Algebra & Analytic Geometry
Unit 6 – Trigonometry
Name & Date
WORD PROBLEM APPLICATIONS
4) A garage is 8 feet above the level street. The driveway from the street to the garage is 45 feet long. Find
the driveway’s angle of incline.
5) A plane flying at an altitude of 33,000 feet is 130 miles away from the airport when it begins its descent.
If the angle of descent (depression) is constant, then find this angle measure. Be careful of the units!
6) An observer on a sea cliff with a height of 12m spots a shark-fin through a pair of binoculars at an angle of
depression of 5.7.
A) To the nearest meter, how far is the shark from the base of the cliff?
B) A few minutes later, the observer spots the same shark at an angle of depression of 7.6. To the
nearest meter, how much closer has the shark moved to the base of the cliff?
7) A ramp is built that leads up to a doorway. Its slope is 1/13. Remember that slope is Rise/Run; find the
angle that the ramp will make with the horizontal?
8) To ensure that water and waste are not trapped in a drain pipe, drain pipes are installed so that every 8 feet
of pipe, there is a drop of 1”. What angle does the pipe make with the horizontal?
9) What is the measure of the angle made by a 200 foot supporting cable with a 150 foot tall cell phone tower?
10) A ski lift is attached to a wire from the base of the mountain to the peak. The wire on the lift is 3,500
feet long and is attached to the ground with an angle of elevation to the top of 25o. What is the height of the
mountain?
Algebra & Analytic Geometry
Unit 6 – Trigonometry
Name & Date
WORD PROBLEM APPLICATIONS
11) An airplane takes off 200 yards in front of a 60 foot building. At what angle of elevation must the plane
take off in order to avoid crashing into the building? Assume that the airplane flies in a straight line and the
angle of elevation remains constant until the airplane flies over the building.
12) During its approach to Earth, the space shuttle’s angle of descent (depression) changes.
A) When the shuttle’s altitude is about 15.7 miles, its horizontal distance to the runway is about 59
miles. What is the angle of descent?
B) When the space shuttle is about 5 miles from the runway, its angle of descent is about 19 degrees.
Find the shuttle’s altitude at this point in its descent.
13) One early escalator built in 1896 rose at an angle of 25 degrees. If the vertical lift was 7 feet, find the
distance a person traveled on the escalator.
14) You are a block away from a skyscraper that is 780 feet tall. Your friend is between the skyscraper and
yourself. The angle of elevation from your position to the top of the skyscraper is 42 0 . The angle of elevation
from your friend’s position to the top of the skyscraper is 71 0 . To the nearest foot, how far are you from
your friend?
15) Susan and Jorge stand 38m apart. From Susan’s position, the angle of elevation to the top of Big Ben is
65 0 . From Jorge’s position, the angle of elevation to the top of Big Ben is 49.5 0 . To the nearest meter, how
tall is Big Ben?
16) The angles of depression to the near and far banks of a river measure 49 and 11, respectively. If the
observer’s eyes are 1.8m above the ground, how wide is the river? Be sure to draw a diagram.