An introduction to Trigonometry

A

An introduction to Trigonometry

A

Opposite

An introduction to Trigonometry

A

OppositeHypotenuse

An introduction to Trigonometry

A

OppositeHypotenuse

Adjacent

Example

Label each of the following triangles

(i) (ii) (iii)

a

c

bf

g

ih

e

d

Example

For the triangle below

a)Write down the lengths of the opposite and hypotenuse sides

b)Work out the ratio Hypotenuse

opposite

8cm

41.8°

12cm

c) Now work out the sin of 42° using the calculator

Opposite = 8cmHypotenuse = 12cm

6666.012

8

Hypotenuse

opposite

Sin 41.8°=0.6665

Right-angled Trigonometry

A

OppHyp

Adj

Hyp

OppSin A

Example

Work out the lettered length in the triangle given below, giving

your answer to 1 decimal place.

a

25°

8 cm

Example

Work out the lettered length in the triangle given below, giving

your answer to 1 decimal place.

b

15 m

48°

Example

Work out the lettered length in the triangle given below, giving

your answer to 2 decimal place.

b 37 cm

15°

Example

Work out the length of AB in the triangle given below, giving your

answer to 2 decimal place.

A

7 mC B

56°

Example

For the triangle below

a)Write down the lengths of the Adjacent and hypotenuse sides

b)Work out the ratio Hypotenuse

Adjacent

7cm54.3°

12cm

c) Now work out the cos of 54.3° using the calculator

Adjacent = 7cmHypotenuse = 12cm

5833.012

7

Hypotenuse

opposite

cos 54.3°=0.5835

Right-angled Trigonometry

A

OppHyp

Adj

Hyp

Adjcos A

Example

Work out the lettered length in the triangle given below, giving

your answer to 1 decimal place.

a

31°

10 cm

Example

Calculate the length of PQ in the triangle PQR

32

52 cm

Q

R P

ExampleCalculate the length XY in the triangle XYZ

59

4.6 cm

Z

X

Y

Right-angled Trigonometry

A

OppHyp

Adj

Adj

Opptan A

Example

Work out the lettered length in the triangle given below, giving

your answer to 1 decimal place.

a

27°

4 cm

ExampleCalculate the length YZ in the triangle XYZ, giving your answer correct to 3 significant figures.

38

4.6 cm

Z

X

Y

Example

Work out the length of AC in the triangle given below, giving your

answer to 2 decimal place.

A

7 mC B

56°