Introduction into trigonometry

Born: 190 BC in Nicaea, Bithynia (now Turkey)Died: 120 BC in probably Rhodes, Greece

Hipparchus of RhodesHipparchus Compiled a trigonometric table for solving triangles. Today we have all the values saved on computers : The calculator!

Example

Work out the lettered lengths for each of the following right angled triangles,

giving your answers to 1 decimal place:

(i)

25°

14 cm

k

47°

21 cma

(ii)

63°

18 cm

b

(iii)

75°21 cm

t

(iv)

9°

5 m

c

(v)

ExampleGiven triangle ABC below work out the length of BC, giving your answer to 3 significant figures.

A B

C

78 mm

59°

Example

A piece of gutter pipe is 350cm long is angled at 6° to the horizontal.

How much higher is the upper end of the guttering than its lower end?

Example

When a set of ladders of length 13m are placed against a vertical wall they

make an angle of 68° with the horizontal.

How far up the wall does the ladder reach?

10cm 10cm

70° 70°

ExampleFor the isosceles triangle below, find the length of the third side, giving your answer correct to 2 decimal places.