Trigonometry is
the study of triangles.
The sides of any right angled triangle can be labelled Hypotenuse, Adjacent
and Opposite.
The hypotenuse is
always opposite the right angle.It is the longest side of the triangle.
The adjacent
is the side that forms part of the
required angle.
The opposite
is the side directly across from the required angle.
The ratio of these sides are given special names:
sine, cosine and tangent.
These are shortened to sin, cos and tan
To find an angle or side , follow this
recipe :-
1. Find and sketch the triangle
2. Mark the right angle
3. Identify and mark angle to be used / found
4. Label Opposite, Hypotenuse and Adjacent
5. Write out ratio
6. Write down solution
Always draw a sketch
Example 1:
Using Tan to find angle
Calculate angle θ˚, the glide path of the aircraft.
Give your answer correct to one decimal
place.
1. Find and sketch the triangle
2. Mark the right angle
3. Identify and mark angle to be used / found
4. Label Opposite, Hypotenuse and Adjacent
Example 2
: Using Tan to find Side
How high above the ground is the aircraft ?
Give your answer correct to one decimal place.
1. Find and sketch the triangle
2. Mark the right angle
3. Identify and mark angle to be used / found
4. Label Opposite, Hypotenuse and Adjacent
5. Write out ratio
6. Write
down solution
The height of the aircraft
is 115.5m (1dp)
Example 3:
Using Sine to find side
A skier is racing down a 150m long ramp.
How high above the ground is the starting
flag ?
1. Find and sketch the triangle
2. Mark the right angle
3. Identify and mark angle to be used / found
4. Label Opposite, Hypotenuse and Adjacent
5. Write out ratio
6. Write
down solution
The starting flag
is 50m above ground.
Example 4
: Using sine to find angle
A skier is racing down a ramp which is 200m
long.
The start of the ramp is 100m above ground
level.
What is the value of θ˚, the angle of the ramp?
1. Find and sketch the triangle
2. Mark the right angle
3. Identify and mark angle to be used / found
4. Label Opposite, Hypotenuse and Adjacent
5. Write out ratio
6. Write
down solution
The angle of the
ramp is 30˚.
Example 5:
Using Cosine to find side
A ship is at anchor. The chain is 150 m
long and makes an angle of 30˚ from the anchor point to the seabed. The anchor
point is 5m above the water level. How deep in the water is the anchor ? Give
your answer to the nearest metre.
solution
Example 6:
Using cosine to find angle
A ship is taut at anchor. The chain is 150
m long and lies 75m from the anchor
point. What is the value of θ˚, the
angle from the seabed to the anchor
point at the ship’s bow ?
Which ratio should I use ?
How high up the wall is the ladder ?
(Give your answer
to 2d.p.)
1. 
Find and sketch the triangle
2. Mark the right angle
3. Identify and mark angle to be used / found
4. Label Opposite, Hypotenuse and Adjacent
5. Write out
6.
Two
Tick Test
Tick what you know Adjacent
Tick what you want Opposite
Look for two ticks 
use that ratio. ( Here, use tan)
7.
Write out
ratio
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Alternative for
credit level
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8.
Write down solution
The ladder is 1.73m (2dp) up the wall.
Using cosine to find hypotenuse
