Here is a link to the same questions but will be much easier to read. Have fun!
Right Angle Trigonometry Word Problems
For
each problem, draw a sketch of the situation, write the equation to solve the
problem and then give the answer.
1. A 10 meter ladder is leaning against
a building. The bottom of the ladder is 5 meters from the building. How many
meters high is the top of the ladder? Round to the nearest tenth. 10 meters
2.
A dog pen is in the shape of a right triangle. The longer leg measures
15 feet. The hypotenuse is 7 feet shorter than three times the length of the
shorter leg. How long is the shorter leg? 8 ft
3.
A guy wire reaches from the top of a 39.32 ft pole to a point on the
ground 15 feet from the pole. Find the length of the wire and the angle it
forms with the ground. 42.ft and 69.12 degrees
4.
A man on a 135-ft vertical cliff looks down at an angle of 16 degrees
and sees his friend. How far away is the man from his friend? How far is the
friend from the base of the cliff? Man-friend
489.8 Cliff-friend 470.8
5.
A road up a hill makes an angle of 5.1 with the horizontal. If the road
from the bottom of the hill to the top of the hill is 2.5 miles long, how high
is the hill? 0.22 miles
6.
A ladder leans against the side of a building. The base of the ladder is
5 meters from the building, and the top is 12 meters above the ground. What is
the length of the ladder and what angle does it form with the ground? 67.4 degrees, 13 meters
7.
A ski resort is installing tows on its new ski runs. One hill has a
vertical height of 500m and is inclined at 42 degrees. Determine the
approximate length of the T-Bar cable if it goes to the top of the hill and
returns?
1494.48 meters
8.
From a point 12 m from the base of a flagpole the angle of elevation to
the top of the pole is 42 degrees. How tall is the flagpole? 10.8 meters
9. A building is 50 feet
high. At a distance away from the building, an observer notices that the angle
of elevation to the top of the building is 41º. How far is the observer from
the base of the building? 57.5 feet
10.
An airplane is
flying at a height of 2 miles above the ground. The distance along the ground
from the airplane to the airport is 5 miles. What is the angle of
depression from the airplane to the airport? 21.8
degrees
11. John wants to measure the height of a tree. He walks exactly
100 feet from the base of the tree and looks up. The angle from the ground
to the top of the tree is 33º. How tall is the tree? 64.94
feet
12. A bird sits on top of a lamppost. The angle of
depression from the bird to the feet of an observer standing away from
the lamppost is 35 degrees. The distance from the bird
to the observer is 25 meters. How tall is the lamppost? 14.3 meters
13. Looking down from the roof of a house at an angle of 23º (angle
of depression) a shiny object is seen. The roof of the house is 32 feet above
the ground. How far is the shiny object from the house? 75.39 feet
14. A tree casts a 60 foot shadow. The angle of
elevation is 30º. This is the angle at which you
look up to the top of the tree from the ground. What is the height of the tree? 34.6 feet
15. A lamp post is 10 feet tall and casts a shadow. The distance
from the top of the lamp post to the tip of the shadow is 20 feet. What is the angle of
elevation at the tip of the shadow on the ground? 30 degrees
16. An observer on top of a 60-foot tall lighthouse sees a boat in
distress at a 5º angle of depression. How far is the boat from the base of the
lighthouse? 685.8 feet
17. A tree casts a shadow 70 feet long at an angle of
elevation of 30º. How tall is the tree? 40.41
feet
18. You are looking up at a fourth story window, 40 feet up in a
building. You are 100 feet away from the building, across the street. What is
the angle of elevation from you to the window? 21.89
degrees
19. A little kid is flying a kite. The string of the kite makes an
angle of 30 degrease with the ground. If the height of the kite is 12 ft, find
the length of the string that the boy has used? 24 feet
20.You are at a
live performance and you are in the balcony. You are looking down at the stage
at an angle of 40 degrees, if you at floor level under the balcony you would be
20 ft away from the stage. How high up is the balcony?
16.8 feet
21. I am standing a point A
on one side of a river and wish to measure the distance across the river to the
corner of a house (H) on the other side.
While facing the house, I turn 90 degrees, I walk exactly 50 feet. I now measure the angle from where I was to
the corner of the house to be 18.23 degrees.
How far it is across the river from point A to the corner of the house? 16.47
22. A guy-wire
must be attached to a 80 foot pole. The
angle that the guy-wire must make with the ground has to be 75.5 degrees. Find the length of the wire required to make
this work? 82.6 feet
23. A device for measuring the cloud height at night
uses a vertical beam of light that makes a spot on the clouds. The spot is viewed from a point 140 feet
along the ground and the angle of elevation is 64.4 degrees. What is the height of the cloud? 292.20 feet
24.
While standing on a cliff 161 feet above the ocean, I see a sailboat in
the distance at an angle of depression of 21.2 degrees. What is the horizontal distance to the
sailboat? 415.1 feet
25.
A wire holding up a 40 foot telephone pole is 48 feet long. The wire is attached to the pole 10.5 feet
below the top. What is the angle of
elevation of the wire? 37.9 degrees
26.
From a window in building A, I observe the top of building B across the
50 foot wide street at an angle of elevation of 74.25 degrees. I also observe the base of the building at an
angle of depression of 52.18 degrees.
What is the height of the building (hint: you will need to do two
calculations and add them) 241.7 feet
