The sine rule is a formula used for calculating either an unknown side length or the size of an unknown angle.

The cosine rule is a formula used for calculating either an unknown side length or the size of an unknown angle.

Using the sine and cosine rules

Maths

In the prior unit, pupils explored the trigonometric ratios for right-angled triangles in a variety of situations. In this unit, pupils explore what can be done when we have a triangle that is not right-angled.

Non right-angled trigonometry

Volume = $$\pi\times r^2\times h$$ where $$h$$ is the height

Volume = $$\frac{h(a+b)}{2}\times l$$ where $$l$$ is the length

What formula is used to find the volume of a cylinder?

$$a=5$$ cm , $$b = 12$$ cm and $$c=$$? cm

$$a=$$? cm , $$b = 24$$ cm and $$c=25$$ cm

$$a=8$$ cm , $$b = $$? cm and $$c=17$$ cm

$$a=11$$ cm , $$b = $$ ? cm and $$c=61$$ cm

Using Pythagoras' theorem, find the missing length when $$c$$ is the hypotenuse and $$b$$ and $$a$$ are the adjacent lengths. 

Using the diagram, work out the correct height and radius.

A plane starts at City X and flies 6 km due north to City A, then turns at a bearing of 059° and travels 11.7km to City B. If the plane flew directly from City X to City B, what is the distance?

A plane starts at an airport and then travels North 12 km, then North East 8.5 km. What is the bearing and distance the plane needs to travel to get back to the airport?

$$\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}$$

Which of the following is the cosine rule?

$$\frac{\sin(A)}{a}=\frac{\sin(B)}{b}=\frac{\sin(C)}{c}$$

Given a triangle with lengths $$a=8$$ cm and angle $$B=36$$° and a length $$c=8$$ cm, work out the missing length to 1 decimal place.

Given a triangle with lengths $$a=8$$ cm and angle $$B=36$$° and a length $$c=10$$ cm, work out the missing length to 1 decimal place.

Given a triangle with lengths $$a=4$$ cm, $$b=6$$ cm and $$c=8$$ cm, work out the angle $$B$$ to 1 decimal place.

Given a triangle with lengths $$a=4$$ cm, $$b=6$$ cm and $$c=4$$ cm, work out the angle $$B$$ to 1 decimal place.

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