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°

5The 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

C

D80 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 km

38°

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

11

6 dm

85°

FE

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 e

6 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 e

6 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