The hypotenuse is the side of a right-angled triangle which is opposite the right angle.

The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.

A cross-section is a 2D face made from cutting straight through any plane of a 3D object.

Applying trigonometric ratios in 3D

Maths

Checking and further securing understanding of Pythagoras' theorem

Using Pythagoras' theorem to justify a right-angled triangle

Calculating the length of a line segment

Checking and securing understanding of the unit circle

Checking and securing understanding of sine ratio problems

Checking and securing understanding of cosine problems

Checking and securing understanding of tangent ratio problems

Calculate trigonometric ratios for 30° and 60°

Calculate trigonometric ratios for 0°, 45° and 90°

Applying trigonometric ratios in context

Applying Pythagoras' theorem in 3D

Advanced problem solving with right-angled trigonometry

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

In the prior unit, pupils were introduced to the trigonometric ratios and developed the skills to ascertain which ratio would be appropriate for a given problem. In this unit, pupils are introduced to a variety of situations where this knowledge is required, such as 3-D problems and elevation/depression.

In this unit, pupils are introduced to a variety of situations where trigonometric ratios are required, such as 3-D problems and problems of elevation or depression.

Right-angled trigonometry

This 3D shape is a cuboid. Work out the length of the dashed line marked, $$x$$, to 1 decimal place.

This 3D shape is a cuboid. Work out the length of the line that the arrow is pointing at (the diagonal of the bottom face), to 1 decimal place.

Which of these calculations are correct for working out the volume of this cuboid?

Work out the length of the edge marked $$x$$ on this triangular prism. Give your answer to 3 significant figures.

The volume of this triangular prism is {{}} $$\text{ cm}^3$$, to 1 decimal place.

$$\frac{1}{3}\times10\times14\times \frac{5}{\cos(64^\circ)}$$

$$\frac{1}{3}\times10\times14\times \frac{10}{\cos(64^\circ)}$$

$$\frac{1}{3}\times10\times14\times 5\tan(64^\circ)$$

$$\frac{1}{3}\times10\times14\times 10\tan(64^\circ)$$

Which of these calculations are correct to find the volume of this right pyramid?

A {{}} is a 3D shape with 6 faces, where there are 3 pairs of congruent rectangles. It also has 8 vertices and 12 edges. 

For which of these triangles, would you use the cosine ratio, to calculate $$x$$?

Which of these calculations are correct to find the length of $$x$$?

Work out $$x^\circ$$ to the nearest degree.

Work out the base angle in this isosceles triangle, to the nearest degree.

This lesson was made for home learning during the pandemic.

Applying trigonometric ratios in 3D

Lesson outcome

This lesson was made for home learning during the pandemic.