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

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.

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.

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