Right-angled Trigonometry

A

Right-angled Trigonometry

A

Opposite

Right-angled Trigonometry

A

OppositeHypotenuse

Right-angled Trigonometry

A

OppositeHypotenuse

Adjacent

Right-angled Trigonometry

A

OppHyp

Adj

Hyp

OppSin A

Right-angled Trigonometry

A

OppHyp

Adj

Hyp

OppSin A

Hyp

AdjCos A

Right-angled Trigonometry

A

OppHyp

Adj

Hyp

OppSin A

Hyp

AdjCos A

Adj

OppTan A

Right-angled Trigonometry

The Old Arab

A

OppHyp

Adj

Hyp

OppSin A

Hyp

AdjCos A

Adj

OppTan A

Right-angled Trigonometry

The Old Arab Sat On His

A

OppHyp

Adj

Hyp

OppSin A

Hyp

AdjCos A

Adj

OppTan A

Right-angled Trigonometry

The Old Arab Sat On His Camel And Hiccupped

A

OppHyp

Adj

Hyp

OppSin A

Hyp

AdjCos A

Adj

OppTan A

Example

Calculate the length of PQ in the triangle PQR

32

52 cm

Q

R P

Example

Calculate the length XY in the triangle XYZ

59

4.6 cm

Z

X

Y

Example

Calculate the length of BC in the triangle ABC.

24

5 cm

A

C

B

Example

A surveyor, P, is 1000m away on

horizontal ground from the foot of a radio

mast, QR. From P the angle of elevation of

the top, R, of the mast is 20. Find the

height of the mast. Assume the surveyor’s

height to be negligible.

Example

From the top of a vertical cliff 100m high

the angle of depression of a boat out at

sea is 32. How far is the boat from the

foot of the cliff?

Example

Calculate the size of angle A in the triangle ABC

6 cm

4 cm

A C

B

Example

Find the size of angle x in each of the following

(i)

4.7 cm

1.2 cm

x

(ii)

10 cm3.7 cm

x

(iii)7 cm

12 cm

x

Example

Calculate the size of angle PQR in the triangle below.

8 cm 8 cm

6 cm

P

RP

Example

The road from village A runs due West for

5 miles to a fort B. A television mast is due

South of B and 4 miles from B. Find the

distance and bearing of the mast from A.

Example

The figure is a pyramid on a square base ABCD. The edges of the base are 30cm long and the height, EH, of the pyramid is 42cm. Find

a) the length of AC

b) the angle EAH

E

C

D

B

A

H

Example

ABCDEF is a prism with a triangular cross-section. , BC = 8m, AB = 6m and CD = 20m.

Find

(i) AC(ii) BD

(iii) the total surface

area of the prism.

A F

E

CB

D