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Trigonometry

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```KS3
Mathematics
Trigonometry Assessment
Calculator
Time allowed: 40 minutes (35 marks)
This is your end of topic assessment.
You should show your workings for all questions.
This test is out of 35 marks.
Question
I can...
1
calculate the missing angle in a right-angled triangle.
2
calculate the missing side in a right-angled triangle.
3
solve simple worded problems.
4
calculate angles of elevation and depression.
5
apply trigonometry to solve bearings problems.
Name: Class: Page 1 of 5
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KS3 Mathematics Trigonometry Assessment
Question 1: Calculate the missing angle.
Give your answers correct to 1 decimal place where appropriate. (Diagrams not drawn to scale)
a.
9cm
6cm
x
b.
9cm
x=
&deg; [2 marks]
x=
&deg; [2 marks]
x=
&deg; [2 marks]
x
4cm
c.
x
3.5cm
2.1cm
[6 marks]
Question 2: Calculate the missing side.
Give your answers correct to 1 decimal place where appropriate. (Diagrams not drawn to scale)
a.
x
5cm
31&deg;
b.
8cm
x=
cm [2 marks]
x=
cm [2 marks]
x=
cm [2 marks]
14&deg;
x
c.
7.5cm
52&deg;
x
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KS3 Mathematics Trigonometry Assessment
d.
5.7cm
x
26&deg;
x=
cm [2 marks]
x=
cm [2 marks]
x=
cm [2 marks]
[12 marks]
e.
x
2.9cm
41&deg;
f.
x
51.5&deg;
4.8cm
Question 3: Worded problems.
Solve the following problems, giving your answers correct to 1 decimal place where appropriate.
a.
An apprentice window cleaner places a ladder of length 4.5m against a wall. The angle that the
top of the ladder makes with the wall is 53&deg;. Work out the distance between the wall and the base
m [2 marks]
b.
A zip line ride starts 55m off the horizontal ground and the length of the ride is 135m. Assuming the
zip line is attached to the ground at the end of the ride, calculate the angle the zip line makes with
the ground.
&deg; [2 marks]
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KS3 Mathematics Trigonometry Assessment
c.
Hamill flies a box kite in an open space. He attaches it to a peg in the ground which is horizontal.
The string is let out to 37m. The kite is 22m vertically off the ground. What angle does the kite string
make with the ground?
&deg; [2 marks]
[6 marks]
Question 4: Angles of elevation and depression.
Solve the following problems, giving your answers correct to 1 decimal place where appropriate.
a.
The top of Mount Snowdon is 1085m above sea level. Carl is looking from sea level and he looks at
the top of the mountain. The angle of elevation is 24&deg; from the horizontal. How far away from the
base of the mountain is he standing?
m [2 marks]
b.
A tourist is looking down from a castle, through a small window, at a mouse on the ground with
an angle of depression of 37&deg;. The mouse is level with the base of the castle, 57m away. Calculate
the height that the tourist is looking from.
m [2 marks]
c.
Ryan and Zack are flying in a hot air balloon. Ryan can see a cow in the field below. He estimates his
horizontal distance from the cow to be 1.2km. The captain says they are flying at an altitude of 500m.
What is Ryan’s approximate angle of depression?
&deg; [2 marks]
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[6 marks]
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KS3 Mathematics Trigonometry Assessment
Question 5: Trigonometry and bearings.
Solve the following problems, giving your answers correct to 1 decimal place where appropriate.
a.
A shark swims on a bearing of 032&deg; for 7.5km.
How far north is the shark from its starting position?
km [2 marks]
b.
A ship sails due east for 27km from point A to point B. It then sails due south for 51km to point C.
Calculate the bearing of C from A.
&deg; [3 marks]
Page 5 of 5
[5 marks]
[Total 35 marks]
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