Advanced problem solving with right-angled trigonometry | Maths

Starter quiz

Work out the length of the hypotenuse, to 1 decimal place.

'8.2 cm' ✓
Work out the length of the missing side of this right-angled triangle, to 1 decimal place.

'12.6 cm' ✓
Work out the length of the line segment AB, where A(-2, -6) and B(1, -10).

'5' ✓
Work out $x$ to 1 decimal place.

'1.9' ✓
Work out the size of the angle, $x$ , to 1 decimal place.

'46.2' ✓
Work out the length of the edge marked $x$ to 1 decimal place.

'7.8 cm' ✓

ABCD is a square on a grid, where each square is 1 unit. Work out the length of BC, to 1 decimal place.

'7.3' ✓
The exact area of the square ABCD is ______ square units.

'53' ✓
Work out the length of CD correct to 1 decimal place.

'20.0 cm' ✓
Work out the perpendicular height of this isosceles triangle, to 1 decimal place.

'8.6 cm' ✓
$Given that FE = 12 cm, EH = 19 cm and angle DHE = <Math>40^\circ</Math>, calculate the volume of the cuboid ABCDEFGH, to the nearest integer.$

Given that FE = 12 cm, EH = 19 cm and angle DHE = $40^\circ$ , calculate the volume of the cuboid ABCDEFGH, to the nearest integer.

'3635 ' ✓
Match the parts of the cylinder to the correct calculation/answer.

radius of the cylinder

⇔

$=18\cos(62^\circ)$ ✓

length of the cylinder

⇔

$=18\cos(28^\circ)$ ✓

volume of the cylinder

⇔

$=(18\sin(28^\circ))^2\times\pi\times18\cos(28^\circ)$ ✓

diameter of the cylinder

⇔

16.9 cm (3 s.f.) ✓

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Sometimes an answer may be best left in an exact form
When dealing with right-angled trigonometry, it is important to look at the information you have and can deduce
Consider whether Pythagoras' theorem or trigonometric ratios are more efficient to use
All models are wrong, but some models are useful

Pupils may not be confident in knowing whether to apply Pythagoras' theorem or a trigonometric ratio.

Encourage pupils to label the diagram with all the information they have and then consider what they can deduce.

Trigonometric functions - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.
Sine function - The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.
Cosine function - The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.
Tangent function - The tangent of an angle (tan(θ°)) is the y-coordinate of point Q on the triangle which extends from the unit circle.