Download Intermediate Pythagoras / Trigonometry Questions GRADE C/B 1. A

Intermediate
Pythagoras / Trigonometry Questions
1.
GRADE
C/B
A wire 18 m long runs from the top of a pole to the ground as shown in the diagram.
The wire makes an angle of 35º with the ground.
18m
35º
Calculate the height of the pole.
Give your answer to a suitable degree of accuracy.
(4)
2.
A
not to scale
30 cm
18 cm
B
D
13.5 cm
C
BDC is a straight line.
Use Pythagoras’ theorem
(a)
to calculate the length of AC,
(b)
to calculate the length of BD,
(2)
(2)
(c)
to show that angle BAC is a right angle.
(2)
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3.
CE = 7.5 cm
A
10 c
m
m
30 c
cm
E
7.5
6 cm
B
The diagram is not drawn to scale.
C
D
Use Pythagoras’ theorem to calculate
(a)
the length of CD,
(b)
the length of CB.
(2)
(3)
4.
BCD is a straight line. CE = 16 cm.
A
32º
16
cm
E
The diagram is
not drawn to scale.
8 cm
x
B
(a)
C
D
Calculate the size of the angle marked x.
(3)
(b)
Calculate the length of AC.
(3)
(c)
Use your answers to parts (a) and (b) to calculate the length of BC.
(3)
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5.
A lift at the seaside takes people from sea level to the top of a cliff, as shown.
Cliff top
B
Not to scale
21 m
23 m
Sea level
A
C
From sea level to the top of the cliff, the lift travels 23 m and rises a height of 21 m.
(a)
Calculate the distance AC.
Answer ...................................... m
(3)
(b)
Calculate angle BCA.
Answer ...................................... degrees
(3)
6.
ABC is a right-angled triangle.
AB = 51 cm
Angle CAB = 48°
B
51 cm
A
48°
Not to scale
C
Find the length of BC.
Give your answer to a suitable degree of accuracy.
Answer ................................................................ cm
(Total 4 marks)
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Task 1:
Which questions require TRIGONOMETRY to be used and which require PYTHAGORAS?
TRIGONOMETRY
Example: 4(a)
PYTHAGORAS
Example:: 2(a)
REMINDER:
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