Trigonometry By MA Year 8

Trigonometry enables you to find missing angles and missing lengths in a triangle using a method called SOHCAHTOA.

Basic Knowledge

S Sin (sin) C Cos (cosine) T Tan (tangent) H Hypotenuse A Adjacent O Opposite

The hypotenuse is the longest side. The opposite is the side opposite the angle being used. The adjacent is the remaining angles.

Which is the Hypotenuse? Which is the Opposite? Which is the Adjacent? Ø H A O

Sin, Cos and Tan are the main functions used in Trigonometry.

S Sin (sin) C Cos (cosine) T Tan (tangent) H Hypotenuse A Adjacent O Opposite

Examples

Example 1: Hypotenuse- X Opposite-15m 35 Adjacent We need to find an equation using the hypotenuse and the opposite. If you cover up the equation we need to find (H), you are left with O/S. So H = 15 divided by sin 35. Answer = 26.2

When to use inverse or shift? As you can see on your calculator there is not only normal sin, cos and tan there is also a shift/inverse version. This is to be used when you are FINDING the angle (in the previous question we were finding a length)

In this equation you need to use inverse. Example 2: 25m 25m Ø 25m 30m We need to find an equation with the adjacent and the hypotenuse. Hypotenuse-25m If you cover up the thing we need to find (C), you are left with A/H. Opposite In this equation you need to use inverse. So, shift cos = 15/25 Answer = 53.1 degrees Ø Adjacent-15m

After doing trigonometry always check the answer looks sensible. Remember: After doing trigonometry always check the answer looks sensible.

How else can trigonometry be used?

Why would you use trigonometry to calculate the height of a tree? You can also use this to find: the height of a cliff, the height of of a mountain etc. Opposite = x 50 Adjacent= 30m

Practise Questions

6m y 2.9m Remember: You are finding the angle.

Answer: y = 61 Degrees

67 14m x Remember: You are finding a length.

Answer: x = 32.98m

I am sitting in a boat 125m from a cliff. If I measure the angle from sea level where I am to the top of the cliff it is 24 degrees. What is the height of the cliff?

Answer: height = 55.65m

What things can be done to make it harder? Use different measurements (use both centimetres and metres etc.) Make them worded questions. Finding angles can be trickier because you have to remember to use inverse. Make it so you have to switch round the equation to get the unknown alone.

Are there any questions?