1 The following diagram shows a triangle with sides 5 cm, 7 cm, 8 cm.
b) Find the area of the triangle.
17.3 cm2 diagram not to scale
a) Find the measure of angle BAC
A
B
C
5 7
860°
2105°
48°C
AB
12m
Find the length of side BC.
25.5 m
337 inches
25°
F
ED 35 inches
Find the length of side DF.
15.7 inches
4 Find the measure of JLK.19 yards
J
LK
18°
12 yards
29.3°
5 The figure shows two adjacent triangular fields ABC and ACD where AD = 30 m, CD = 80 m, BC = 50m. ADC = 60° and BAC = 30°
a) Calculate the length AC.
b) Calculate the size of ABC 50 m
AB
CD80 m
30 m
30°
60°AC = 70m
ABC 44.4°
612 Q
P
R
11
8Find the measure of PRQ.
63.1°
7 Find the area of quadrilateral ABCD:
113 cm2
8 Determine the area of:
7.3km
9.4 km38°
21.1 km2
9 The diagram shows the plan of a playground with dimensions as shown.
C
B
A
4 8 m
5 7 m
11 7 º
Calculate the length BC
89.7 m
10 From point A, the angle of elevation to the top of a tall building is 20°. On walking 80 m towards the building the angle of elevation is now 23°. How tall is the building?
23°20°BA 80m
204 m
116 dm
85°F
E
D
38°Find the length of side EF.
8.17 dm
12 The diagram shows the plan of a playground with dimensions as shown.
C
B
A
4 8 m
5 7 m
11 7 º
Calculate the area of triangle ABC
1220 m2 (3 s.f.)
13 In the diagram, triangle ABC is isosceles. AB = AC, CB = 15 cm and ACB is 23°.
Find the length of AB.
A
C B23º
15 cm
8.15 cm
14 A triangle has sides of length 7cm and 13cm and its area is 42cm2. Find the size of its included angle.
67.4°
15 In triangle ABC, find the measure of angle B given that A = 46, a = 7 cm, and b = 12 cm
No solution
16 The following diagram shows the side view of a tent. The side of the tent AC is 6 m high. The ground AB slopes upwards from the bottom of the tent at point A, at an angle of 5° from the horizontal. The tent is attached to the ground by a rope at point B, a distance of 8 m from its base.
A
B
C
ro p e6 m
8 m5 °
Calculate the length of the rope, BC.
9.57 (3 s.f.)
17
38.6°
The following diagram shows the side view of a tent. The side of the tent AC is 6 m high. The ground AB slopes upwards from the bottom of the tent at point A, at an angle of 5° from the horizontal. The tent is attached to the ground by a rope at point B, a distance of 8 m from its base.
A
B
C
ro p e6 m
8 m5 °
Calculate the angle CBA that the rope makes with the sloping ground.
18 In triangle ABC, find the length of c given that b = 45 m, A = 56 and B = 72
c = 37.3 m
19 In triangle ABC, find the measure of angle B given that a = 14, A = 41, and b = 18
B = 57.5 or 122
20 An aircraft takes off from an airport and flies 400 km in the direction 040°. It then changes course and flies in a direction 160° for 500 km.a) How far away is the aircraft from the airport?b) Find the bearing of the aircraft from its starting
point.
40°
160°
400 500
a) 458 kmb) 111°
Homework
• Review Set 10A, pg349– #10, 12, 13
• Review Set 10B, pg351– #8, 9, 10
• Review Set 10C, pg352– #1, 8-12