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

Checking and securing understanding of trigonometric ratios

Drawing the sine and cosine graphs

Drawing the tangent graph

Interpreting the trigonometric graphs

The area of any triangle

Calculating the area of any triangle when the height is not known

The cosine rule

Using the sine and cosine rules

Considering the appropriate trigonometric rule

Problem solving with non right-angled trigonometry

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.

In this unit, pupils explore how to apply knowledge in trigonometry to non right-angled triangles.

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$$^2$$.

Starter Quiz

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