Applying trigonometric ratios in context | Maths | Quizalize & Oak National Academy

Starter quiz

Which of the trigonometric ratios should you use to calculate $x$ ?

sine

cosine ✓

tangent
Which of the trigonometric ratios should you use to calculate $x$ ?

sine ✓

cosine

tangent
Work out the length of $x$ , to 1 decimal place.

'10.2 cm' ✓
Work out the length of $x$ , to 1 decimal place.

'6.9 cm' ✓
Work out the size of $x$ , to the nearest degree.

'55' ✓
Which of these calculations will find the value of $x$ ?

$x=8\tan(41^\circ)$

$x=\frac{8}{\tan(41^\circ)}$ ✓

$x=8\tan(49^\circ)$ ✓

$x=\frac{8}{\tan(49^\circ)}$

Exit quiz

A helicopter flies so that it is 6 miles due East and 2 miles due North of where it started. Which calculation finds the angle, $x$ to fly direct?

$x=\tan\left(\frac{2}{6}\right)$

$x=\tan\left(\frac{6}{2}\right)$

$x=\arctan\left(\frac{2}{6}\right)$ ✓

$x=\arctan\left(\frac{6}{2}\right)$
A helicopter flies so that it is 2 miles due East and 6 miles due South of where it started. What is the angle, $x$ , to the nearest degree to fly direct?

'72' ✓
$A helicopter flies on an angle of <Math>38^\circ</Math> direct to its destination, such that it is 4 miles due East of the start position. How far is the direct distance, to the nearest mile?$

A helicopter flies on an angle of $38^\circ$ direct to its destination, such that it is 4 miles due East of the start position. How far is the direct distance, to the nearest mile?

'5' ✓
$A helicopter flies on an angle of <Math>38^\circ</Math> direct to its destination, such that it is 4 miles due East of the start position. How far North of the start is it, to the nearest mile?$

A helicopter flies on an angle of $38^\circ$ direct to its destination, such that it is 4 miles due East of the start position. How far North of the start is it, to the nearest mile?

'3' ✓
A search and rescue helicopter spots a person out at sea. Using the diagram, work out the height of the helicopter above the sea level, to the nearest metre.

'1834 m' ✓
Using the diagram (not to scale), work out the height of the tree, to 1 decimal place.

'11.6 m' ✓

Worksheet

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Lesson Details

Key learning points

Trigonometric ratios are used in many scenarios
Trigonometric ratios are used to calculate the height of a structure

Common misconception

Using the wrong trigonometric function.

Encourage pupils to draw the right-angled triangle for the scenario if they are unsure so that they can label the sides and be confident about which trigonometric function is needed.

Keywords

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.