int 1 h'work chapter 16.cwk (wp) - montrose acad...

©TeeJay Publishers 2007 page 63 Trigonometry

1. Make a sketch of the triangles shown below and mark on each triangle the hypotenuse, the opposite and the adjacent sides to the angle.

a b c

2. Use the tangent (or tan) button on a scientific calculator to find the following tangents (correct to two decimal places) :–

a tan 40° b tan 44·5° c tan 89·8°.

3. Look at this right angled triangle with ∠ABC = 20°.

a What is the length of the opposite side ?

b What is the length of the adjacent side ?

c Divide :- (opp ÷ adj) to get tan 20°.

d Look up tan 20° on your calculator to check you get the same answer.

1. Make a sketch of this right angled triangle.

COPY and complete to calculate the size of the opposite side :–

tan B =

opp

adj

=> tan 34° = x10

=> x = 10 x tan 34°

=> x = ..... cm (to 1 dec place)

Chapter 16Trigonometry

Exercise 16.1

Exercise 16.2

x°x°

x°

11 cm20°

A

B C

4 cm

x cm

10 cm

34°

A

B C

adj


2. Use the method shown on the previous page to calculate the length of the opposite side (x cm) of each triangle. (Give each answer to 1 decimal place.)

a b c

3. The angle of elevation of the top of a tree from a point 21 metres from its foot is 19°.

Calculate the height of the tree.

4. A hill runs up from a main road to the house at the top.The hill makes an angle of 12° to the road.

Calculate how high the house is above the road.

1. Use the correct buttons on YOUR calculator to find the sizes of the angles A, B and C (to the nearest degree) :-

a tan A = 1·376 b tan B = 0·445 c tan C = 0·052.

2. Make a sketch of this right angled triangle.

COPY and complete the following to calculate the size of ∠PQR to 1 decimal place.

tan Q =

opp

adj

=> tan x° = 1210

=> tan x° = .......

=> x = ... (to 1 dec. pl.)

∠PQR = .........

40°

65° 48°

x cm x cm

x cm11 cm

6 cm

10 cm

Exercise 16.3

19°h m

21 m

12°

hillh m

35 m

road

12 cm

10 cm

x°

P

Q R


3. Use the method shown on the previous page to calculate the size of the anglemarked in each triangle. (Give each answer to 1 decimal place.)

a b c

4. Ross is 180 centimetres tall. In the sunshine, he casts a shadow on the ground 260 centimetres long.

Find the angle of elevation (x°) of the sun.

5. What is the angle of elevation of the top of a bell tower 150 feet high, from a point on level ground

30 feet from the base of the tower ?

a°

b°

c°

15 cm

15 cm 8 cm

7 cm12 cm

5 cm

x °

260 cm

180 cm

150 ft

x °

Exercise 16.4

1. Use the sine (or sin) button on your scientific calculator to calculate the following, correct to two decimal places :–

a sin 10° b sin 60° c sin 81·5°.

2. Use the correct buttons on your calculator to find the sizes of the angles A, B and C (to the nearest degree) :-

a sin A = 0·423 b sin B =

1

8c sin C =

11

12.

3. Use the sine ratio in these triangles to find the size of the opposite side in each case. (Give each answer to 1 decimal place.)

a b c

20 cm18 cm

27 cm

x cmx cm

x cm

20°

65° 82°

30 ft


4. A kite is flying at an angle of 73° to the groundand is attached to a taut string 100 metres long.

Calculate the height of the kite above the ground.

5. A funicular railway is 275 metres long and the angle between the railway and the ground is 14°.

Calculate the height (h metres) of the top of the railway above the ground.

6. Use the sine ratio in these triangles to calculate the size of the angles asked for.(Give each answer to 1 decimal place if necessary.)

a b c

7. A pencil 12 cm long lies with its end just restingagainst the end of a book 7 cm thick.

Calculate the angle between the table and the pencil (x°).

8. A plank is 2·5 metres long and is just touching the top of a wall, 1·61 metres in height.

Calculate the angle between the plank and the ground.

73°

h m 100 m

14°

275 mh m

22 cm16 cm

25 cm

11 cm

a°14 cm

b°c°

7 cm

x°

12 cm7 cm

x°

2·5 m1·61 m


Exercise 16.5

1. Use the cosine (or cos) button on your scientific calculator to calculate the following, correct to two decimal places :–

a cos 12° b cos 30° c cos 78°.

2. Use the correct buttons on your calculator to find the sizes of the angles A, B and C (to the nearest degree) :-

a cos A = 0·788 b cos B =

1

5c cos C =

7

8.

3. Use the cosine ratio in these triangles to find the size of the adjacent side in each case. (Give each answer to 1 decimal place.)

a b c

4. Calculate the size of angle a, b and c in each of these triangles :-(Give each answer to 1 decimal place.)

a b c

5. A telephone pole has a support cable 5·4 metres long attached from its top to a point on the ground, 4·5 metres along from the base of the pole.

Calculate the angle the cable makes with the ground.

6. The angle between the sloping roof on this hut and the horizontal is 23°.

The sloping roof is 3·1 metres long.

Calculate the width of the hut.

18 cm

x cm48°

19° 64°

x cm

24 cm15 cm

x cm

18 cm

16 cm

22 cm

9 cm

a°12 cm

b°

c°

8 cm

23°

3·1 m

x cm

5·4 m

x°

4·5 m


Exercise 16.6

1. Use the correct ratio from SOHCAHTOA to find the value of x in each case. (Give each answer to 1 decimal place.)

a b c

d e f

2. This picture shows a lamp-post 5·3 metres long, whichhas toppled over and come to rest against the top of awall, 4·2 metres high.

Calculate the size of the angle (x °) between thelamp-post and the ground.

3. A plank, just touching the top of a wall, is 6·5 metres long.

Calculate how far away the foot of the plank is from the wall.

4. This flag is in the shape of aright angled triangle.

Calculate the size of the angled marked x in the flag.

14 cmx cm

20°

x cm72°

12 cm

65°

x cm

9 cm

x°

7·5 cm22 cm

x°

11 cm

22 cm

x°

12 cm

16 cm

4·2 m 5·3 m

x°

wall

30°

6·5 m

h m

x°

50 cm

20 cm

SO

H CAH T

OA


Revision Exercise

1. Use your calculator to find the following (to two decimal places) :-

a sin 68° b cos 30° c tan 7°.

2. Use your calculator to find the sizes of the angles a, b, and c.

a sin a° = 0·866 b cos b° = 0·545 c tan c° = 0·649.

3. Use the correct ratio from SOHCAHTOA to find the value of x in each case. (Give each answer to 1 decimal place.)

a b c

d e f

4. Calculate the height of the tree.

5. A bus is parked next to a cable supportingthe bus park floodlights.

This cable makes an angle of 74° with the ground.

The cable is fixed at a point 2·5 metres from the base of the pole.

Calculate the height of the floodlight pole.

6. The steps to the large slide are 5·2 metres long.The bottom of the steps is 3·8 metres from a

metal support pole.

Calculate the size of the angle (x), between the steps and the ground.

10 cm

x cm

14°

x cm

69°

11 cm74°x cm

8·2 cm

x°

9 cm

17 cm

x°

13 cm

19 cm

x°

20 cm

18 cm

5·2 m

3·8 m

x°

74°

2·5 m

25°

4·2 mh m

int 1 h'work chapter 16.cwk (wp) - montrose acad...

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