Sine and Cosine Examples & Practice Questions

Here are some Sine and Cosine worked examples. There will then be some questions for you to practice.

Enjoy!

There are FOUR question types where the sine and cosine rules would be applied. Learn these rules and it will come easily to you.

Number 1: Two angles given plus any side = SINE RULE needed

Number 2: Two sides given plus an angle not enclosed = SINE RULE needed

For the example above there is still more to do. You need to do sin-1(0.36) =21.1° which is the answer!

Please note for this example I have already rearranged the sine rule. I have flipped the formula so that the angles 'A' and 'B' are on the top of the formula and 'a' and 'b' are on the bottom.

Number 3: Two sides given plus the angle enclosed = COSINE RULE needed

Please note here that I have used the 'normal' form of the cosine rule.

Number 4: All three sides given but no angles = COSINE RULE needed

Please note that here I have used the rearranged version of the cosine rule.

These are four examples of the ways you can use the sine and cosine rule. This is a grade A topic.

PRACTICE QUESTIONS

Q1- Find the side x in each question. Give your answer correct to 1 decimal place.

a)

b)

Q2- Find the angle x. Give your answer to the nearest degree.

c)

Q3- Find x or θ in each case

d)

e)

f)

g)

ANSWERS



a)

b)

c)

I have not yet worked out the answers to d, e, f, and g but when I have I will insert them below!

Amelia :)

Sine and Cosine Rules

Normal trigonometry using SOH CAH TOA etc. can only be applied to right-angled triangles. For non right-angled triangles we use the Sine and Cosine rules.

Step 1: Labelling the Triangle

Here is how you should label your triangles. It doesn't matter which side you call a, b, and c (as long as the angles are labelled properly). Also, which ever angle you label 'A' you must label the opposite side 'a'.

Step 2: Choosing Which Formula to Use

The Sine Rule

Please note that you don't use the whole thing with both '=' signs. You just choose the two parts you want, depending on how you have labelled your triangle.

The Cosine Rule
There are two forms. The 'normal' form is:

The form for finding and angle is:

Please note that you do not have to memorise this formula. You can simply rearrange it from the formula you are given in the front of your maths paper.

Area of a Triangle
This formula is used when you know two sides and the angle between them:

If you use this formula then it is easiest if you label the angle that you are given 'C' so you can easily substitute it into the formula.

Please also note that you already know a simple formula for calculating the area which is 1/2(base x height). The formula here is used for when you don't have those values.

Thank you for reading this blog post. My next post will be Sine and Cosine rule worked examples.
Amelia