GCSE Mathematics AWS

Exact Values of Sin

and Cos

Answers

GCSE Mathematics FG19 HG19 1.

Prove that the value of Sin 30˚ = 1 2 60° Answer:

30°

22 - 12

Hyp 2

2

60°

60°

Find the value of Answer: Opp Hyp

Sin

3

Sin 30 = 1 2

Opp

1

given that Sin

= Opp Hyp

= Cos

= Cos

Adj Hyp

=

So Opp = Adj 3.

=

60°

2

2.

Adj

2

Sin

Triangle is isosceles, so

= 45˚

Find the value of x in the following triangle:

Answer:

Opp

Hyp Sin 8.5cm

= Opp Hyp

x

Sin 30 = x 8.5

8.5 x Sin 30 = x 8.5 x 0.5 = x 4.25cm = x

30°

4. Find the perimeter of the triangle ABC. Give your answer in the form a + b√c. Cos

Answer:

Adj

A

B 60°

Opp

= Adj Hyp

Cos 60 = Adj 10 10 x 1 = Adj 2

10m

5 = Adj C

Sin

= Adj Hyp

Sin 60 = Opp 10 10 x 3 = Opp 2 5 3 = Opp

Perimeter = 10 + 5 + 5 3 = 15 + 5 3 m

Exact Values of Sin

and Cos

Answers

GCSE Mathematics FG19 HG19

Higher tier only 5.

A skating ramp has angle of 30° to the horizontal. Find the length of the ramp leaving your answer in the form a b

Answer: Cos

= Adj Hyp

Cos 30 = 3 Hyp Hyp =

30°

3 √3 2

= 3÷ 3 = 3x2 = 6 x 2 3 3

3m

3 =6 3=2 3m 3 3

Higher tier only 6.

Knowing that the area of the triangle is 48cm2, find the length of x.

Answer:

Area of

=

48

=

1 x 12 x 2



48

=

6 x



48

=

3

=

16cm

12cm

30° x

1 ab Sin C 2 Sin30

x 1 2