Problem solving with non right-angled trigonometry | Maths

Starter quiz

Trigonometric functions are commonly defined as __________ of two sides of a right-angled triangle for a given angle.

ratios ✓

examples

particles

difference
Which of these formulae are the sine rule or correct rearrangements of the sine rule?

$\sin(A)=\frac{a\sin(B)}{b}$ ✓

$\frac{b}{\sin(b)}=\frac{c}{\sin(C)}$ ✓

$\frac{a}{\sin(A)}=\frac{c}{\sin(C)}$ ✓

$\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}$ ✓

$\frac{a}{\sin(b)}=\frac{b}{\sin(C)}$
A triangle has vertices $A, B$ and $C$ , and corresponding lengths $a, b$ and $c$ . $C$ = 39.6°, $c$ = 6.4 cm and $a$ = 9.4 cm. Work out acute angle $A$ to 1 significant figure.

'70°' ✓
An isosceles triangle has two lengths of 9.22 cm and the third length 14 cm. Work out the angle between the two equal lengths. Give your answer to 1 decimal place.

'98.8°' ✓
An isosceles triangle with lengths 8.6 cm, 8.6 cm and $x$ cm has two base angles of 54.5°. Work out the perimeter of the triangle to 1 decimal place.

'27.2 cm' ✓
The area of a regular hexagon is 93.5 cm $^2$ . Work out the perimeter of the regular hexagon to the nearest integer.

'36 cm ' ✓

A square has a diagonal length of 8.49 cm. The area of the square, to the nearest integer, is ______ cm $^2$ .

'36' ✓
A rectangle has two diagonals. The length of each diagonal is 13.4 cm. The diagonals intersect to create two obtuse angles of 127°. Work out the longest length of the rectangle to 2 s.f.

'12 cm' ✓
A rectangle has two diagonals. The length of each diagonal is 13.4 cm. The diagonals intersect to create two obtuse angles of 127°. Work out the perimeter to the nearest integer.

'36 cm ' ✓
A rectangle has two diagonals. The length of each diagonal is 9.5 cm. The diagonals intersect to create two obtuse angles of 143°. Work out the perimeter to the nearest integer.

'24 cm' ✓
A triangle has three lengths; 11.3 cm, 12.7 cm and 17.0 cm. Identify the three angles.

90°, 48.3° and 41.7° ✓

48.4°, 81° and 50.6°

41.6°, 53.5° and 84.9°

90°, 34° and 56°
A triangle has three lengths; 10.3 cm, 15.8 cm and 8 cm. Identify the three angles when rounded to 3 s.f.

119°, 26.3° and 34.8° ✓

119°, 30° and 31°

26.3°, 40.5° and 113.2°

34.7°, 56.9° and 88.4°

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Pupils may think that they have to use the sine or cosine rule.

Encourage pupils to consider all the trigonometric knowledge they have and choose the most appropriate piece for the problem they are dealing with.

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.