Choosing an appropriate method for finding lengths of a triangle | Maths

Starter quiz

In a right triangle, if the hypotenuse is 40 cm and a second side is 32 cm, what is the length of the third side? (Use a calculator to help you.)

24 cm ✓

26 cm

22 cm
In a right triangle, if the shortest sides are 10 cm and 7.5 cm, what is the length of the hypotenuse? (Use a calculator to help you.)

12.5 cm ✓

11.5 cm

13.5 cm
Would a triangle ABC with sides AB = 9cm, BC = 7.5cm, AC = 12.5cm be similar to the one shown in the diagram?

Yes

No ✓
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.
In a right triangle, if the hypotenuse is 200 cm and a second side is 120 cm, what is the perimeter? (Use a calculator to help you.)

470 cm

492 cm

480 cm ✓
In a right triangle, if the hypotenuse is 30 cm and a second side is 18 cm, what is the area? (Use a calculator to help you.)

$512 cm^2$

$216 cm^2$ ✓

$1028 cm^2$

This robot standing on a box has a fly on the top of their head. How high up (h) is the fly from the ground?

3.2 m ✓

3.9 m

4.1 m
This robot standing on a box has an ant on the top of their head. How high up (h) is the ant from the ground to 2 d.p. ?

4.06 m ✓

3.20 m

4.65 m
If the area of square ABCD is $25 cm^2$ , what is the length of the diagonal BD to 2 d.p. ?

7.07 cm ✓

6.06 cm

8.08 cm
A rectangle ABCD has length 6cm, and the diagonal angle ABC is 38ᵒ. What is the height of the rectangle to 2 d.p. ?

4.69 cm ✓

4.28 cm

5. 83 cm
A rectangle ABCD has length 12cm, and the diagonal angle ABC is 40ᵒ. What is the area of the rectangle to 2 d.p. ?

$120.83 cm^2$ ✓

$130.83 cm^2$

$140.83 cm^2$
Given all angles and the base of an isosceles triangle, what trigonometric function could be used to find the height of the triangle most efficiently?

Tangent ✓

Sine

Cosine

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Pupils may struggle to find a right-angled triangle within the context of the question.

Encourage the pupils to sketch the question and consider adding a perpendicular line to the diagram.

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