  # Solve Trigonometry Problems

In this worksheet, students will apply Pythagoras' Theorem and trigonometry within 3D shapes. A requirement of higher level maths is to apply more than one skill within the same question. Key stage:  KS 4

GCSE Subjects:   Maths

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

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Triangle Mensuration

Difficulty level:   #### Worksheet Overview Ever wanted to fly a fast jet or passenger aircraft.  Well if you do you will need to be good at trigonometry

Angles and distances are an everyday part of a pilots jobs.

If you ask a pilot if they are happy in their jobs, they would probably say it has its ups and downs.

Engineers and designers would also use trigonometry a great deal in their work.

Lets recap on your trigonometry ratios.  oh and would you believe it our mate Pythagoras gets in on the act.  He can't help himself can he.

Pythagoras' Theorem

a² + b² = c²

I wonder if pilots ever think about him when the fly over Greece.

The trig ratios are often combined with Pythagoras's Theorem when solving problems relating to right angled triangles.

Lets have a go   Figure 1 just asks the question, that may well be all that you are given.

Figure 2 Draw in the right angled triangle.

Figure 3 Mark in the angle.  Remember it is the middle letter A.

Pythagoras' Theorem has also been applied in figure 3 to find the length of the diagonal.  We need this before we can calculate the angle.

30 cm² + 10 cm² = √1000 = 31.622..... cm

Mark this on the diagram to help see the trig ratio that you need.

20 ÷ 31.6222 = 0.63246...... tan-1 0.63246 = 32.3° correct to 1 decimal place.

There is quite a lot to take in here so take it one step at a time.

### What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started 