Maths Skills

If you do not have a Scientific Calculator then this website will be useful https://www.rapidtables.com/calc/math/Tan_Calculator.html

You will need to use a Calculator in your Paper One exam so if you do not own one then perhaps you could borrow one from a friend?

Pythagoras' Theorem - section 4 (p58) of textbook

To use the Pythagorean theorem formula, we need to know the length of any two sides in a right angled triangle. We can then rearrange the formula to find the side we are looking for.

So, if we take the formula:

a² + b² = c²

We can rearrange it to help us find the length we’re missing:

To find the length of Side A: a² = c² – b²
To find the length of Side B: b² = c² – a²
To find the length of Side C: c² = a² + b²

Most of the questions you will be asked will most likely use Trigonometry (Pythagorus thereom). If the question has an Angle given then you will most likely use Trigonometry. Click the Button below to better understand Trigonometry from the Khan Academy. Use SOHCAHTOA to remember!

Trigonometry

They will usually ask questions that use a Right Angle Triangle and so the formulae below should be revised. SOHCAHTOA

In simple terms if you need to know the length of a line then use Sin, Cos, Tan. If you need to know an angle then use Sin-1, Cos-1, Tan-1

Examples

This maths question is worth 7 marks. Immediately looking at the information given you will need to use Trigonometry as there is an Angle and a Length given.

First step is to look at the diagram as a right angled triangle - see sketch diagram.

Then you need to work out the length of the diagonal line (Hypotenuse). This will be done by using Sin as we know the Adjacent (b) to be 700 and we know the angle of 60. Therefore we can use Sin 60 = 700 / C.

Sin 60 = 0.8660254 to 2 decimal places = 0.87

So your formula is 0.87 = 700 / C

This can be rewritten as C = 700 / 0.87

C = 808.29

Next, you need to find a. Now that you have two measurements (b and c) you can use Pythagorus

a2 + b2 (700) = c2 (808.29)

So to find the length of a you need to move b to the opposite side of the = . This makes a2 = c2 - b2.

This looks like a2 = 808.29 (squared) - 700 (squared)

a2 = 163332.7241

Therefore a = (square root) 404.14

So now you know the length of the distance between the brackets with the height at 700mm. Next you need to know the width of a when the height becomes 720. You can use Pythagorus again to work this out as you know two lengths but not the angle. Therefore, apply the formula again a2 + b2 = c2.

a2 + 720 (squared) = 808.29 (squared)

a2 = 653,332.724 - 518,400

a2 = 134932.724

a = (square root) 134932.724 = 367.33

Therefore the change of distance between the two brackets is 404.14 - 367.33 = 36.81

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