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Find a Missing Angle Using the Sin Rule

In this worksheet, students will apply the sin rule to find out angles within a non-right angled triangle

'Find a Missing Angle Using the Sin Rule' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Triangle Mensuration

Difficulty level:  

Worksheet Overview


Did you know that trigonometry can be used to calculate the position from the shore to a ship?

The person on the shore can find the angle between the shore and the ship and the ships captain can find the angle from the ship to shore.  Looks a bit like a pirate ship to me so best we can locate their exact position in case we need help.

We had better get a move on.


Trigonometry is the study of angles and dimensions of triangles.

We only tend to see it as trying to solve problems in a triangle within a maths lesson.

Until the day we are on the high seas we had best learn the  formula.


The sin rule is used to calculate angles in a non right angled triangle.  And here it is.

It looks the same as the sin rule for finding a side length. The difference is that they have been turned upside down with the angles (SIN) being on the top.


You will need a scientific calculator in order to get the sin-1 button. Make sure it is set to degrees.

Example 1


sin rule for missing angle

The triangle is labelled in capital letters, with the opposite side to them labelled in lower case letters.

Getting the opposite side labelled correctly is key here.

We want angle b.

The only other information we have is angle A, side a and side b.


Our formula therefore is      SIN A          =    SIN B  

                                                a                     b


Substitute in what we know  SIN 98        =   SIN B 

                                                8.3                   6


Now for the geeky bit

We need to get  SIN B on its own, so we need to rearrange the formula.  We move 6 up to SIN98 to get:


6 x sin98  = 5.941...... do this first to get an answer THEN divide by 8.3 = 0.7158

Now because we are looking for an angle we need the sin-1 button. (Press shift then sin on your calculator)


and viola ....45.7° (to 3 significant figures)


NOTE: If you try to put it all into the calculator at once the rules of bidmas aren't followed and your answer will be incorrect.


Example 2

We need SIN B   =  SIN C  

                   b            c


Substitute in what we know  SIN 37      =  SIN C

                                                 6                 5

Bring 5 up to up to sin37  to give us 5 x sin37  =  3.009 ÷ 6 = 0.501

sin-1 = 30.1°( to 3 significant figures)


Let give it a try..

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