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Trigonometri

This document contains 18 multi-step trigonometry word problems involving sin, cos, and tan functions. The problems provide diagrams of geometric shapes and ask the learner to use trigonometric ratios to find unknown angle measures, side lengths, or functional values. Example problems include finding sin(x) given information about a midpoint, finding the length of a side given a trigonometric ratio, or calculating an unknown using two given trigonometric ratios. The goal is to use properties of 30-60-90 and 45-45-90 triangles and trigonometric functions to solve for unknown values in right triangles and other geometric shapes.

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Sashineka Sumbulingam
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369 views12 pages

Trigonometri

This document contains 18 multi-step trigonometry word problems involving sin, cos, and tan functions. The problems provide diagrams of geometric shapes and ask the learner to use trigonometric ratios to find unknown angle measures, side lengths, or functional values. Example problems include finding sin(x) given information about a midpoint, finding the length of a side given a trigonometric ratio, or calculating an unknown using two given trigonometric ratios. The goal is to use properties of 30-60-90 and 45-45-90 triangles and trigonometric functions to solve for unknown values in right triangles and other geometric shapes.

Uploaded by

Sashineka Sumbulingam
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOC, PDF, TXT or read online on Scribd
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161

TRIGONOMETRY (1)
[ TYPE 1 ]
1

In the diagram, B is the midpoint of straight line AC.

Find the value of sin x.

(Ans :

3
5

)
[2 marks]

Answer :

In the diagram, PQRS is a trapezium, and SR = RQ.

Find the value of sin SPQ.

(Ans :

12
13

)
[2 marks]

Answer :

162
3

In the diagram, PQRS is a square.

Find the value of sin PTR.

12
13

(Ans :

)
[2 marks]

Answer :

In the diagram, PQR is a right angled triangle.

Find the value of cos .

(Ans :

8
17

)
[2 marks]

Answer :

163
5

The diagram shows a right angled triangle EFG and DEF is a straight line.

Find the value of cos x.

(Ans :

1
2

)
[2 marks]

Answer :

In the diagram, D is the midpoint of AC and AE =

Find the value of cos y.

(Ans :

5
6

3
BC.
4

)
[2 marks]

Answer :

164
7

In the diagram, M is the midpoint of the straight line FG.

Find the value of tan x.

(Ans :

2
3

)
[2 marks]

Answer :

In the diagram, B is the midpoint of the straight line ABC dan CD =

Find the value of tan y.

(Ans :

9
8

2
AE.
3

)
[2 marks]

Answer :

165
[ TYPE 2 ]
9

In the diagram, ABC is a right angled triangle.

Given that sin x =

5
, find the length, in cm, of BC.
13

(Ans : 10)

[2 marks]
Answer :

10

In the diagram, PQR is a right angled triangle.

Given cos PRQ = 0.6, find the length, in cm, of PQ.

(Ans : 8)
[2 marks]

Answer :

166

167
[ TYPE 3 ]
11

In the diagram, PQR is a right angled triangle.

Given that tan x =

5
, find the value of cos x.
12

(Ans :

12
13

)
[2 marks]

Answer :

12

In the diagram, QRS is a straight line.

Given that QS = 12 cm, and tan x = 0.8. Find the value of sin .

(Ans :

5
13

)
[2 marks]

Answer :

168

169
13

In the diagram, QRS is a straight line.

Given that cos x =

4
, find the value of tan y.
5

(Ans :

2
3

)
[2 marks]

Answer :

14

In the diagram, LMN is a straight line.

Given that sin x =

3
, find the value of tan y.
5

8
(Ans : 11
)

[2 marks]
Answer :

170
15

The diagram shows two right angled triangles, ABC and BCD.

Given that cos x =

3
, find the value of sin y.
5

(Ans :

5
13

)
[2 marks]

Answer :

16

In the diagram, PQRS is a square, PQT and UPS are straight lines

Given that sin y =


[2 marks]
Answer :

3
, find the value of tan x.
5

(Ans :

4
7

171

[ TYPE 3 ]
17

In the diagram, QTS is a straight line.

Given that sin x =

4
12
and tan y =
, calculate the length, in cm, of TS.
5
5

(Ans : 7)
[2 marks]

Answer :

18

In the diagram, PTR and SRQ are straight lines.

Given that tan y = 2, PR = 30 cm and SQ = 23 cm. Calculate the length of TR.

(Ans : 16)
[2 marks]

Answer :

172

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