Topics covered within this unit: 34·1 Pythagoras revision 34·2 Trigonometric ratios
34·3 Using your calculator to work with trigonometric ratios
[1CA30.58]
34·4 Finding missing sides and angles 34·5 Trigonometry in the real world
The Learning Outcomes covered in this unit are contained in the following sections:
GT.3b GT.4 34·1 Pythagoras revision
Key words Trigonometric ratios
Opposite Adjacent
Angle of elevation Angle of depression Clinometer
By the end of this section you should: ● recall how to use Pythagoras’s theorem to fi nd the lengths of the sides of right-angled triangles
We learned about Pythagoras’s theorem in Section B, Unit 22. In that unit, we used the theorem to fi nd the unknown third side of a right-angled triangle when we knew the other two sides. We also learned in Unit 31 that Pythagoras's theorem can be used to fi nd the distance between two points.
Theorem 14 (Pythagoras’s theorem): In a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
c a b
Pythagoras’s theorem can be written in one short equation: c2
= a2 + b2
c is the hypotenuse, (longest side of the triangle) and a and b are the other two sides.
Section C Applying our skills 539
Trigonometry
Something to think about …
For safety, windows can be fi tted with window restrictors to prevent them from opening too far.
Standard window restrictors, extend the window to a maximum angle of 50° and allow the window to be opened no more than 100 mm.
Calculate the height of the window shown, given that the restrictor in the diagram is a standard restrictor.