Download Trig Ratio Word Problems

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Using Trig. Ratios to solve Real World Problems

Draw a diagram to represent the problem.

Label it carefully and clearly mark out the quantities that are given and those which
have to be calculated.
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Identify the appropriate trigonometric ratio to use.
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Solve the equation for the unknown variable.
Depression and Elevation.
If a person on the ground looks up to the top of a building, the angle formed between the
line of sight and the horizontal is called the angle of elevation.
If a person standing on the top of a building looks down at a car on the ground, the angle
formed between the line of sight and the horizontal is called the angle of depression.
Examples.
1. The angle of depression from the top of a tower to a boulder on the ground is 38º. If the
tower is 25m high, how far from the base of the tower is the boulder
2. From a point 80m from the base of a tower, the angle of elevation is 28˚. How tall is the
tower?
3. A ladder that is 20 ft. is leaning against the side of a building. If the angle formed
between the ladder and ground is 75˚, how far is the bottom of the ladder from the base
of the building?
4. When the sun is 62˚ above the horizon, a building casts a shadow 18m long. How tall is
the building?
5. A kite is flying at an angle of elevation of about 55˚. Ignoring the sag in the string, find the
height of the kite if 85m of string have been let out
6. Given sin  
6
, find cos  90   and sin  90   .
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Additional Practice- Practice setting up and solving words requiring the use of trig. ratios
1. A ladder 14 feet long rests against the side of a building. The base of the ladder rests on level
ground 2 feet from the side of the building. What angle does the ladder form with the ground?
2. A 24 foot ladder leaning against a building forms an 18 degree angle with the side of the building.
How far is the base of the ladder from the base of the building?
3. A road rises 35 feet for every 400 horizontal feet. What is the measurement of the angle the road
forms with the horizontal?
4. A kite is held by a taut string pegged to the ground. The string is 40 feet long and makes a 33
degree angle with the ground. Supposing that the ground is level, find the vertical distance from
the ground to the kite.
5. A wire anchored to the ground braces a 17 foot pole. The wire is 20 feet long and is attached to
the pole 15 feet from the base of the pole. What angle does the wire make with the ground?
6. A jet airplane begins a steady climb of 15 degrees and flies for 2 ground miles. What was its
change in altitude?
7. A cable is used to support a 245 meter TV tower. If the angle the cable makes with the ground is
78 degrees, how long is the cable?
8. A 32 foot ladder leaning against a building touches the side of the building 26 feet above the
ground. What is the measurement of the angle formed by the ladder and the ground
9. The 600 block of Powell Street in San Francisco has a steep rise. If it takes 66 feet along the
horizontal for the street to rise 10 feet, find the angle the street makes with the horizontal.
10. A guy wire is attached to a tower at a point 100 feet above the ground. If the tower is
perpendicular to the ground and the wire makes and angle of 55 degrees with the ground, find the
length of the wire.
11. A bird watcher is standing 50 feet from the base of a large tree. The surveyor measures the angle
of elevation to a bird on top of the tree as 71.5°. How tall is the tree?
12. The angle of depression from the top of a tower to a boulder on the ground is 38º. If the tower is
25m high, how far from the base of the tower is the boulder?
13. A rocket is launched at an angle into outer space. After a minute, the rocket traveled 5 miles and
had an altitude of 3.5 miles. What is the angle of elevation that the rocket was launched at?
14. Tom went to a park that is the shape of a square. If he runs a total of 8 miles around the park, how
far would have it been if he ran diagonally across the park?
15. Your car is driving up a hill that is 500 feet long at an angle of elevation of 15o. What is the vertical
distance covered by your car to the nearest foot?
16. The computers on an airplane broke to the pilot has to land the plane by herself. If the planes
altitude is 15,000 feet and the plane is 10,000 feet from the beginning of the runway, what angle of
depression must she take to get to the beginning of the runway?
17. A construction worker leans his ladder against a building making a 60o angles with the ground. If
his ladder is 20 feet long, how far away is the base of the ladder from the building?
18. The bottom of a double rainbow is going over a tree that is 18 feet tall. If you’re standing feet from
the tree, what is the angle of elevation to the bottom of the rainbow?
19. The outline of a teepee is shaped like an equilateral triangle. If the sticks on the side are 12 feet
long how tall is the teepee?
20. The directions for the use of a ladder recommend that for maximum safety the ladder should be
placed against a wall at a 75 degree angle with the ground. If the ladder is 14 feet long, how far from
the wall should the base of the ladder be placed?
21.
a. B = 90°
4
3
cos A  ,sin A 
5
5
b.
Find cos. C, sin C, and tan C