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Grade 11 Mathematics
Page 1 of 3
Applications of Sine and Cosine Law (hints only)
Date:
B
1. In parallelogram ABCD, the lengths of the sides are 22 cm and
65 cm. If the length of the diagonal is 77 cm, determine the
area of the parallelogram.
A common question is, “Which diagonal?” It’s
important to realize that it doesn’t matter!
65 cm
C
77 cm ?
22 cm
or is BD 77 cm ?
A
Why?
D
2. Three circles with centres A, B, and C are mutually tangent and no circle lies inside of another circle. The circle
with centre A has radius 3 cm and the circle with centre B has radius 5 cm. If ∠BAC = 60° , determine the
radius of the third circle and the area of ∆ABC .
3
A
5
B
K
60°
3
5
x
x
C
3. Two ships leave a harbour, H, the first at 12:00 and the second at 12:30. The first ship sails on a course of
N30°E at a speed of 20 km/h. The second ship sails on a course of S20°E at 15km/h.
a) Determine the distance between the two ships at 14:30 to the nearest km.
b) Determine the radar bearing from the first ship to the second ship.
no diagram; messy diagram; small diagram; no
labels in your diagram
Common problems:
Understand the problem.
RHHS Mathematics Department
Grade 11 Mathematics
Page 2 of 3
Applications of Sine and Cosine Law (hints only)
Date:
F
F
12
10
8
θ
6
4
2
H
-2
50 km
30 °
20 km /h for
2.5 h
30°
x
H
5
15 km /h
for 2 h
130°
30 km
-4
20°
-6
-8
S
S
4. Two concentric circles have centre C. Two points A and B are located on the smaller circle, with radius 10 cm, so
that ∠ACB = 52° . Point M is located on the larger circle so that ∠CAM = 150° and ∠CBM = 135° .
Determine the radius of the larger circle, accurate to one decimal.
C
∠ ACB=52 °
∠ CBM=135 ° C
B
B
CP=10
P
A
∠ CAM=150 °
P
M
CM=?
Understand the problem.
Then this diagram might be too
small to be useful.
Draw another “sterilized” diagram
that helps you solve...
RHHS Mathematics Department
M
CM = ???
A
Grade 11 Mathematics
Page 3 of 3
Applications of Sine and Cosine Law (hints only)
Date:
5. Two fire towers are located 100 km apart on hills at points T and R. The bearing from T to R is northeast. A fire,
F, is observed from tower T at N10°E and from tower R at N75°W. The town of Valleyview, at point V, is on a
bearing of N25°E from T and S70°W from R. The observers report that the wind is blowing the fire directly
toward Valleyview at 8 km/h. How much time do the town officials have in order to evacuate the town of
Valleyview?
Understand the problem.
This one also needs 2 diagrams, each bigger than your hand!
F
N75°W
N10°E
R
F
S70°W
35°
V
R
25°
V
135°
N25°E
TR=100 km
15°
TR=100 km
20°
45°
T
Fig. 1: the diagram using the info given
45°
T
Fig. 2: Solve for the angles, as shown.
6. In right triangle ∆RST , ∠T = 90° . A point Q is located inside the triangle above base ST, such that SQ = 20 =
TQ and ∠QST = 30° . If the measure of ∠R = 20° , determine the length of RQ, accurate to one decimal
place.
Understand the problem.
Draw and label a diagram.
If your labels are smaller than 10 pt font, draw it larger!
Notice that ∆QTS is divided into two 30-60-90˚ triangles; producing TS.
RHHS Mathematics Department