Pythagoras and Trigonometry: notes

Pythagoras' Theorem

• Rule: in a right-angled triangle, a^2 + b^2 = c^2, where c is the hypotenuse, the side opposite the right angle.
• Finding the long side: add the squares, then square root. Sides 3 and 4 give 9 + 16 = 25, so c = 5.
• Finding a short side: subtract the squares. Hypotenuse 13 and side 5 give 169 - 25 = 144, so the other side is 12.
• Common triples: 3, 4, 5; 5, 12, 13; 8, 15, 17.

Right-Angled Trigonometry

• SOH CAH TOA: sin = opposite / hypotenuse, cos = adjacent / hypotenuse, tan = opposite / adjacent.
• Label first: name the sides from the angle you are using.
• Finding an angle: use the inverse button. If tan x = 1, x = 45 degrees.
• Exact values: sin 30 = 1/2, cos 60 = 1/2, tan 45 = 1.
• Elevation and depression: angles measured from the horizontal, up or down.

Any Triangle

• Sine rule: a / sin A = b / sin B.
• Cosine rule: a^2 = b^2 + c^2 - 2bc cos A.
• Area: 1/2 ab sin C.
• Choose: use the sine rule when you have a matching angle and side pair; use the cosine rule for two sides and the angle between them, or three sides.