The area is the size of the surface and states the number of unit squares needed to completely cover that surface.

The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.

The area of any triangle

Maths

Checking and securing understanding of trigonometric ratios

Drawing the sine and cosine graphs

Drawing the tangent graph

Interpreting the trigonometric graphs

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

The sine rule

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

A triangle with perpendicular height =  10  cm and base = 9  cm

A triangle with perpendicular height =  6  cm and base = 3  cm

A triangle with perpendicular height =  1  cm and base = 2  cm

A triangle with perpendicular height =  2  cm and base = 2  cm

Match the areas of these triangles with their dimensions. 

A right-angled triangle has a height of 13 cm and a hypotenuse of 20 cm. The area of the triangle to 1 decimal place is {{}}cm$$^2$$.

A triangle has two adjacent lengths of 8 cm and 9 cm with an angle in between of 53°. The area of the triangle to 1 decimal place is {{}}cm$$^2$$.

Area = $$\frac{1}{2}ab\text{sin}C$$, despite a, b and C being explicit in the formula, they just mean two adjacent sides and the angle between them. Select other formulas for the area.

The adjacent lengths are 7 cm and 9 cm with a 47° angle in between.

The adjacent lengths are 12 cm and 6 cm with a 47° angle in between.

The adjacent lengths are 3 cm and 4 cm with a 90° angle in between.

The adjacent lengths are  1 cm and 6 cm with a 53° angle in between.

The adjacent lengths are 6 cm and 6 cm with a 60° angle in between.

Match the areas with the dimensions of the triangle. 

Six equilateral triangles are put together to make a regular hexagon. The length of each triangle is 6 cm. Work out the exact area of the regular hexagon. 

Match the polygon with the formula for calculating its area.

A triangle with perpendicular height =  5  cm and base = 6  cm

A triangle with perpendicular height =  10  cm and base =  8 cm

A triangle with perpendicular height =  3  cm and base =  4 cm

A regular hexagon is made up of 6 equilateral triangles. The total area of the regular hexagon is 120 cm$$^2$$. The area of one triangle is {{}}cm$$^2$$.

A right-angled triangle has a height of 8 cm and a base of 5 cm. Work out the length of the hypotenuse to 1 decimal place.

A right-angled triangle has a height of 4 cm and a hypotenuse of 15 cm. Work out the length of the base to 1 decimal place.

A rectangle has a width of 5 cm and a diagonal length of 13 cm. The area of the rectangle is {{}}cm$$^2$$.

This lesson was made for home learning during the pandemic.

The area of any triangle

Lesson outcome

This lesson was made for home learning during the pandemic.