Problem solving with right-angled trigonometry | Maths

Starter quiz

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

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

'8.5 cm' ✓
Work out the length of the line segment AB, where A(2, 6) and B(5, 10).

'5' ✓
Work out $x$ to 1 decimal place using the tangent ratio.

'8.7' ✓
Work out the size of the angle, $x$ .

'30' ✓
Work out the length of the edge marked $x$ to 1 decimal place.

'3.6 cm' ✓

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

'5.4' ✓
Which of these calculations are correct for finding the area of the square ABCD?

$7^2-4\times\left(\frac{2\times5}{2}\right)$ ✓

$2\times10+3^2$

$2^2+5^2$ ✓

$(\sqrt{2^2+5^2})^2$ ✓

$4\times\left(\frac{2\times5}{2}\right)-7^2$
Match the edge with the correct calculation.

AE

⇔

$=\frac{16}{\tan(71.6^\circ)}$ ✓

DC

⇔

$=\frac{16}{\sin(71.6^\circ)}$ ✓

FG

⇔

$=HC+\frac{16}{\tan(71.6^\circ)}$ ✓
Given that this is an isosceles triangle, calculate the angle marked $x$ to 1 decimal place.

'74.7' ✓
$The area of this isosceles triangle is <span class="blank">______</span> <Math>\text{cm}^2</Math> to 3 significant figures.$

The area of this isosceles triangle is ______ $\text{cm}^2$ to 3 significant figures.

'118' ✓
$Given that AB is the diameter of the circle, the area of the circle is <span class="blank">______</span> <Math>\text{cm}^2</Math> to 3 significant figures.$

Given that AB is the diameter of the circle, the area of the circle is ______ $\text{cm}^2$ to 3 significant figures.

'331' ✓

Loading worksheet ...

Loading presentation ...

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

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.