Trigonometry By MA Year 8 Trigonometry enables you

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.

Ø H A Which is the Hypotenuse? Which is the Opposite? Which is the Adjacent? 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-15 m 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)

Example 2: 25 m Ø 30 m 25 m We need to find an equation with the adjacent and the hypotenuse. If you cover up the thing we need to find (C), you are left with A/H. In this equation you need to use inverse. So, shift cos = 15/25 Answer = 53. 1 degrees Ø Adjacent-15 m Opposite Hypotenuse-25 m

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

Practise Questions

6 m y 2. 9 m Remember: You are finding the angle.

Answer: y = 61 Degrees

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

Answer: x = 32. 98 m

I am sitting in a boat 125 m 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. 65 m

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?