Problem solving with trigonometry | Maths | Quizalize & Oak National Academy

Starter quiz

In a right triangle, if the shortest sides are 48 cm and 20 cm, what is the length of the hypotenuse?
- 52 cm ✓
- 50 cm
- 54 cm
Which of the following statements is true for these triangles?
- The triangles are similar. ✓
- The triangles are not similar.
- It is not possible to know whether the triangles are similar or not.
In a right triangle, if the hypotenuse is 45 cm and a second side is 36 cm, what is the length of the third side? (Use a calculator to help you.)
- 28 cm
- 27 cm ✓
- 26 cm
In a right triangle, if the hypotenuse is 15 cm and a second side is 12 cm, what is the perimeter? (Use a calculator to help you.)
- 34 cm
- 36 cm ✓
- 32 cm
For this pair of triangles, can you determine whether they are similar without using side lengths?
- Yes, because their three angles correspond. ✓
- No because you only know two angles.
- No, because you always need a side and two angles.
Could an equilateral triangle be similar to the triangle below?
- Yes
- No ✓

Isosceles triangle ABC has base 4 cm and ∠ABC = ∠BCD = 30ᵒ. What is the height of the triangle to 2 d.p. ?
- '1.15 cm' ✓
Isosceles triangle ABC has base 9 cm and ∠ABC = ∠BCD = 42ᵒ. What is the height of the triangle?
- '4.05 cm' ✓
What is the area of an equilateral triangle of side 4 cm to 2 d.p. ?
- '3.46' ✓
Isosceles triangle ABC has base 4 cm and ∠ABC = ∠BCD = 20ᵒ. What is the area of the triangle to 2 d.p. ?
- '1.46' ✓
Isosceles triangle ABC has base 5 cm and ∠ABC = ∠BCD = 24ᵒ. What is the perimeter of the triangle to 2 d.p. ?
- '9.57' ✓
A yacht sails 50 km due East and then 60 km due South. If the yacht is still facing South, how many degrees clockwise (2d.p.) should it turn to be facing directly towards its starting point.
- '140.19' ✓

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Pupils may struggle to identify a right-angled triangle in the problem.

Encourage pupils to sketch the question out and add any known right angles or perpendicular lines, as this may lead to a right-angled triangle.

Trigonometric ratios - The trigonometric ratios are ratios between each pair of lengths in a right-angled triangle.