1. by P Rowell Tile Hill Wood School
Trigonometry
by P Rowell Tile Hill Wood School

2. Triangles -the basics In any triangle the three angles add up to 180°
One of the angles in a right angle triangle is 90°
The hypotenuse is the side opposite the right angle and is always the longest side of a right angle triangle

3. Pythagoras
In any right angle triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. h2 = a2 + b2 h a b

4. Naming the sides  hypotenuse hypotenuse opposite adjacent  adjacent
The hypotenuse is always the side opposite the right angle.
The opposite and adjacent sides are dependent on where the angle  is

5. Trigonometry

6. Trigonometry

7. Trigonometry

8. Trigonometry

9. Trigonometry

10. Trigonometry – The Sine Ratio
For a given angle  the ratio of the opposite side and the hypotenuse is always the same.
We call this ratio the Sine Ratio
The sine ratio links three things the size of an angle , the length of the side opposite the angle and the length of the hypotenuse.
If we are given the values for two of these we can find the value of the third

11. Example
Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long
12m h
40°

12. Example
Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long
Hyp
12m h
Opp
40°
Adj
Step 1: Label the sides

13. Example
Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long
Hyp
12m h
Opp
40°
Adj
Step 1: Label the sides
Step 2: Cross out the side you don’t need

14. Example
Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long
Hyp
12m h
Opp
40°
Adj
Step 1: Label the sides Step 2: Cross out the side you don’t need Step 3: Decide which ratio you need to use O
SOH CAH TOA
S X H

15. Example
Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long
Hyp
12m h
Opp
40°
Adj
Step 1: Label the sides Step 2: Cross out the side you don’t need Step 3: Decide which ratio you need to use
Step 4: Cover up what you want to find O 
S X H

16. Example
Find the height of a kite when it is flying at an angle of 40° and the kite string is 12m long
Hyp
12m h
Opp
40°
Step 4: Cover up what you want to find
Step 5: Write down the calculation 
S X H