Download Part B - Concept Determine whether you should use

MPM2D
Unit #6 - Trigonometry
Sine & Cosine Law
Part B - Concept
Determine whether you should use the sine law or the cosine law to solve each
triangle.
Sine Law or
Cosine Law?
Diagram
5.1 cm
H
3.6 cm
I
5.2 cm
G
a)
K
70°
3.7 cm
L
59°
J
b)
N
5.0 cm
72°
M
4.4 cm
O
c)
Q
5.6 cm
P
45°
4.8 cm
R
d)
Reason
MPM2D
Date ______________
Sine Law and Cosine Law - Applications
1. A ship is sailing a course from A to B, past a lighthouse at C. The
angles are <A= 45O and <B= 55O. If the distance from A to B is 6km,
find AC and BC. (5 km, 4.3 km)
A
A
B
C
C
B
2. Chuck Wagon is building a cottage. The width of the cottage is
20m. On one side the angle of the roof is 25O and on the other
side the angle is 70O. Find the lengths of the rafters (AB and AC).
(18.9 m, 8.5 m)
20m
3. Sandy Beach is standing on the shore of a lake at C.
He knows the distance CA is 3 km, CB is 2.5 km and
the angle at C is 70O. Find the width of the lake, AB.
(3.2 km)
B
A
C
4. A hockey net is 2m wide. A player shoots from a point where the puck is 13m
from one goal post and 12m from the other goal post. Within what angle
must she make her shot to hit the net? (8O)
12m
13m
?
5. Two hunters, Frank and Buck, are hiding in a
swamp. They are 100m apart. A duck lands in the
water. The angles formed are shown. Find the
distance between Buck and the Duck. (66.5m)
1
40O
Frank
65O
Buck
6. Ray Dar runs a radar station. From
his station the bearing of a plane
100 km away, is N 40O E. Another
plane is on a bearing of N 45O W
and is 220 km away. Find the
distance between the two planes.
(233.6km)
N
220 km
45
O
O
40
100 km
W
E
Station
7. Patty Cake and Jim Nasium are flying a
kite. Patty is 200 m away from Jim who
is holding the kite. Facing Jim, Patty
finds the angle of elevation of the kite is
40O. If the kite string makes an angle of
85O with the ground, find the amount of
string let out by Jim. (156.9m)
Jim
40O
85O
200m
Patty
8. Town A is 80km west of town B. From
town A, the angle the elevation to a
satellite is 45O and the angle of
elevation from town B is 60O. Both
towns are on the same side of the
satellite. How far is the satellite from
town B? (218km)
45O
A
60O
80 km
B
9. Two roads from the Quebec town of
Deux Rues are at an angle of 15O.
Yves Trough takes one road and
walks at 5 km/h, while Dwain Pipe
takes the other road and walks at 3
km/h. How far apart are Yves and
Dwain after 2 hours? (4.5 km)
Yves
Dwain
15O
2
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