Trigonometric Ratios Worksheet Page 21
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22B
11. Bill started at point A and walked
22 m to a point B, then walked 17 m
5. An air traffic controller is tracking two
to a point C, and then walked back to
airplanes, flying at the same altitude, on
point A. The path of his walk formed
the radar screen. Airplane A, en route to
a triangle with ∠BAC = 42°. Leslie
Saskatoon, is 23.8 km away in a direction
calculated that the distance Bill walked
60° west of north. Airplane B, en route
from point C to point A was 24.9 m.
to Calgary, is 25.2 km away in a direction
Kelly calculated that the distance that
70° west of north.
Bill walked from point C to point A
a) Draw a diagram to illustrate this
was 7.8 m.
situation.
a) Do you think that Leslie’s, Kelly’s, or
b) How far apart are the two airplanes?
both girls’ calculations are correct?
b) Draw a diagram to represent Leslie’s
6. Building plans show a triangular cottage
calculations for the distance Bill
property with side lengths 42.7 m,
walked from point C to point A.
49.4 m, and 58.2 m.
c) Draw a diagram to represent Kelly’s
a) Sketch a diagram of this property.
calculations for the distance Bill
b) Determine the angles formed
walked from point C to point A.
between the sides of the triangular
d) Explain the differences between
property.
Leslie’s calculations and Kelly’s
calculations.
7. A funnel is in the shape of a right circular
cone. The angle at the vertex of the cone
12. Faiza would like to calculate the height
is 36°. Find the diameter of the funnel at
of a cliff. From point A where she is
a point on the face 6 in. from the vertex.
standing, the angle of elevation to point
C at the top of the cliff is 38°. If Faiza
8. Two ships, A and B, both started out
walks 80 m east to point D, △ABD is
at point C. Ship A is now 40 km from
formed, where B is the base of the
point C in a direction 30° west of north.
cliff, such that ∠DAB = 47° and
Ship B is now 60 km from point C in a
∠ADB = 49°.
direction 40° west of south. Determine
the distance between the two ships.
C
C
9. Two checkpoints, A and B, in an
orienteering course are 5 km apart.
Another checkpoint, C, is 3 km from
B
B
checkpoint A. The angle between AB
and AC is 25°. Determine the distance
between checkpoints B and C.
38°
38°
49°
49°
47°
47°
A
A
D
D
10. The pendulum on a clock is 30 cm long.
80 m
80 m
The pendulum moves a horizontal
a) Determine the height, BC, of the
distance of 5 cm from one end of each
cliff.
swing to the other. Find the angle
through which the pendulum swings.
b) Determine the distance from point A,
where Faiza is standing, to point C at
the top of the cliff.
978-0-07-090893-2 Mathematics for College Technology 12 Study Guide and Exercise Book • MHR 21
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