There are three ratios that you need to learn:

sino

yp

pp

h cos

a

yp

dj

h tan

o

dj

pp

a

Where are the hypotenuse, adjacent and opposite lengths.

This is opposite the right-angle

This is next to the angle

This is

opposite th

e angle.

30

10cmx

You need to label all the lengths of the triangle.

The adjacent is not needed in this

question; the question is only using

opposite and hypotenuse.

30

10cmx

You need to label all the lengths of the triangle.

The adjacent is not needed in this

question; the question is only using

opposite and hypotenuse.

30

10cmx

sino

yp

pp

h cos

a

yp

dj

h tan

o

dj

pp

a

We need to use the sine ratio and substitute the values/variables that we know.

sino

yp

pp

h

sin 3010

x

30

10cmx

sino

yp

pp

h

* sin 3010

x

We need to solve the equation (*).

We can think of this as: 5

sin30

sin3

10

0 01

x

OR

rearrange the equation (*) by multiplying both sides by x. sin 30

11 10

00

x sin 010 3 x

5 x

These two triangles are very different.

The variable x will be on the

denominator

sino

yp

pp

h

sin 3010

x

This is an example of where we have to solve an equation with the variable on the denominator, so multiply both sides by x.

sin 3010

xx x

sin 3 100x still need to get x on its own, so divide both sides by sin30

s 0

10

in3x

5

10

0. 20

15cm

x

tano

dj

pp

a

30

tan3015

x xx

tan 3 150x tan 30 tan30

15cm

x30

tano

dj

pp

a tan30

15

x

tan 3015

x xx

tan 3 150x

t 0

15

an3x