Applying trigonometric ratios in 3D | Maths | Quizalize & Oak National Academy

Starter quiz

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

'cuboid' ✓
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 $x$ ?

$x=5.5\sin(42^\circ)$

$x=5.5\cos(42^\circ)$

$x=5.5\tan(42^\circ)$ ✓
Work out $x$ to 1 decimal place.

'26.7' ✓
$Work out <Math>x^\circ</Math> to the nearest degree.$

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

'32' ✓
Work out the base angle in this isosceles triangle, to the nearest degree.

'69' ✓

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

'21.5 cm' ✓
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.

'17.4 cm' ✓
Which of these calculations are correct for working out the volume of this cuboid?

$18\times19\times34$

$18\times19\times19\sin(34^\circ)$

$18\times19\times19\cos(34^\circ)$

$18\times19\times19\tan(34^\circ)$ ✓
Work out the length of the edge marked $x$ on this triangular prism. Give your answer to 3 significant figures.

'7.51 cm' ✓
$The volume of this triangular prism is <span class="blank">______</span> <Math>\text{ cm}^3</Math>, to 1 decimal place.$

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

'420.4' ✓
Which of these calculations are correct to find the volume of this right pyramid?

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

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

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

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

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If angles are involved, then you may wish to apply trigonometric ratios to the 3D problem
This allows you to calculate the angle between the line and the plane
It can also be used to find missing lengths if the angle is known

Trigonometric ratios cannot be applied to 3D shapes.

Pupils may benefit from imaging the cuboid is 'sliced' through and a triangle drawn on the now visible face.

Hypotenuse - The hypotenuse is the side of a right-angled triangle which is opposite the right angle.
Trigonometric ratios - The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.
Cross-section - A cross-section is a 2D face made from cutting straight through any plane of a 3D object.