Trigonometry in the Real World
1.
A guy wire is attached to the top of a vertical tower and to and anchor point on
the horizontal ground 20m from the base of the tower. The guy wire makes an
angle of 75° with the ground. Draw a sketch of this situation and determine the
height of the tower to the nearest metre.
2.
A ladder is 3.0m long and it is leaning against a wall. The foot of the ladder
makes an angle of 76° with the ground. How far up the wall is the top of the
ladder? Draw a sketch and give the length of the ladder to the nearest metre.
3.
Sam is flying a kite. She has let out the string to a length of 210m. The string
makes an angle of 48° with the horizontal. The string is taut and Sam’s hand is
1.45m above the ground.
a.
Draw a sketch of this situation
b.
What is the vertical height of the kite from Sam’s hand?
c.
How high is the kite above the ground?
4.
Harry and Mike conducted an experiment to determine the angle of elevation to
the sun. Harry held a 100cm ruler vertical on level ground and it cast a shadow
52cm long. Draw a sketch of this situation and calculate the angle of elevation of
the sun to the nearest degree.
5.
A ladder is 3.5m long and is leaning against a wall. The foot of the ladder is 1.0m
from the wall. Draw a sketch of this situation and determine the angle the ladder
makes with the floor to the nearest degree.
6.
A helicopter is hovering 6000m above the ground. A searchlight on the ground is
a horizontal distance of 1700m from the helicopter.
a.
Draw a sketch of this situation
b.
The searchlight is aimed so that its beam shines on the helicopter.
Calculate the measure of the angle of elevation of the helicopter from the
searchlight.
7.
Radar tells an air-controller that an approaching plane is at an altitude of 800m
and that the angle of approach relative to the ground is 21.5°. Draw a sketch of
this situation and determine the distance from the plane to the control tower to
the nearest metre.
8.
A group of students measured a distance on the ground of 50m from the base of
a flag pole. If the angle of elevation to the top of the flagpole is 17°, what is the
height of the flagpole? Draw a sketch and solve the height to the nearest metre.
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Foundations for College Mathematics (MAP 4CC)
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Trigonometry in the Real World
9.
An architect is designing a house with a garden. The wall length is 30m and a
thick garden hedge, 55m long, is planted at an angle from the edge of the wall.
What angle does the hedge form with the wall? Draw a sketch of this situation
and solve the angle to the nearest degree.
10.
Two buildings are 50m apart. From the top of the shorter building, the angle of
depression to the foot of the taller building is 27°. The angle of inclination from
the top of the shorter building to the top of the taller building is 7°. Calculate the
height of both buildings. Draw a sketch to help you.
11.
Two trees are 100m apart. From a point half-way between them, the angles of
elevation to their tops are 12° and 16°. How much taller is one tree than the
other? Draw a sketch to help you solve this problem.
12.
A storm causes some 14.0m hydro poles to lean over. One pole leans at an
angle of 72° with the ground. How far is it from the ground to the top of the pole?
Draw a sketch to help you solve this problem.
13.
A roller coaster climbs vertically 60m at an angle of 25° from the lowest to the
highest point on the track. It then plunges over the high point to begin the ride.
Calculate the length of the track that takes the roller coaster from the ground to
the highest point.
14.
A boat sails North away from a harbor at a speed of 15km/hr. 2 hours later, the
boat turns due East at a speed of 20km/hr. How far is the boat from the harbor
after 3 hours? Draw a sketch of this situation and solve the distance to the
nearest km.
15.
A ramp rises vertically 1.5m for every 10m of horizontal distance. Draw a sketch
and determine the angle of inclination of the ramp to the nearest degree.
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Foundations for College Mathematics (MAP 4CC)
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