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

The sine rule

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

For calculating either an unknown side length or the size of an unknown angle

Identify the correct ways to express $$p$$ using the diagram.

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

Which of the following are correct versions of the sine rule?

Length $$a$$ is opposite angle A. Work out the size of length $$a$$ giving your answer to 2 decimal places.

Length $$b$$ is opposite angle B. Work out the size of length $$b$$ giving your answer to 2 decimal places.

Work out the size of angle $$\alpha$$ giving your answer to 1 decimal place.

$$\text{hyp}\times\sin(\theta°)=\text{opp}$$

$$\theta°=\arcsin\left(\frac{\text{opp}}{\text{hyp}}\right)$$

$$\text{hyp}=\frac{\text{opp}}{\sin(\theta°)}$$

$$\text{hyp}=\frac{\sin(\theta°)}{\text{opp}}$$

Which of the following are equivalent to $$\sin(\theta°)=\frac{\text{opp}}{\text{hyp}}$$?

Using $$\sin(A)=\frac{p}{c}$$, identify all the rearrangements.

Using $$\sin(C)=\frac{p}{a}$$, identify all the rearrangements.

An isosceles triangle has lengths 10 cm, 10 cm and 16 cm. The area of the isosceles triangle is {{}}cm$$^2$$.

An equilateral triangle has lengths of 10 cm. The area of the triangle, to 1 decimal place, is {{}}cm$$^2$$.

A regular hexagon has lengths of 6 cm. The area of the hexagon, to the nearest integer, is {{}}cm$$^2$$.

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