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Choosing an appropriate method for finding lengths of a triangle

I can choose the appropriate method to find the missing side in a right-angled triangle.

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Lesson 11 of 12

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Year 9

Choosing an appropriate method for finding lengths of a triangle

I can choose the appropriate method to find the missing side in a right-angled triangle.

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Lesson details

Key learning points

Trigonometry can be useful in many practical situations.
You can use it to find the height of objects.
You can use it to find the length of an object given the length of its shadow.
Sometimes it may be better to use Pythagoras' theorem.

Keywords

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

Common misconception

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.

This lesson can be made into a practical, where pupils could estimate the height of a tree or a building, either by using similar triangles or trigonometry with a clinometer.

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Licence

This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Worksheet

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Prior knowledge starter quiz

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6 Questions

Q1.
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.)

Correct answer: 24 cm

26 cm

22 cm

Q2.
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.)

Correct answer: 12.5 cm

11.5 cm

13.5 cm

Q3.
Would a triangle ABC with sides AB = 9cm, BC = 7.5cm, AC = 12.5cm be similar to the one shown in the diagram?

Yes

Correct answer: No

Q4.
For this pair of triangles, can you determine whether they are similar without using side lengths?

Correct answer: Yes, because their three angles correspond.

No because you only know two angles.

No, because you always need a side and two angles.

Q5.
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

Correct answer: 480 cm

Q6.
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.)

$$512 cm^2 $$

Correct answer: $$216 cm^2 $$

$$1028 cm^2 $$

Assessment exit quiz

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6 Questions

Q1.
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?

Correct answer: 3.2 m

3.9 m

4.1 m

Q2.
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. ?

Correct answer: 4.06 m

3.20 m

4.65 m

Q3.
If the area of square ABCD is $$25 cm^2$$, what is the length of the diagonal BD to 2 d.p. ?

Correct answer: 7.07 cm

6.06 cm

8.08 cm

Q4.
A rectangle ABCD has length 6cm, and the diagonal angle ABC is 38ᵒ. What is the height of the rectangle to 2 d.p. ?

Correct answer: 4.69 cm

4.28 cm

5. 83 cm

Q5.
A rectangle ABCD has length 12cm, and the diagonal angle ABC is 40ᵒ. What is the area of the rectangle to 2 d.p. ?

Correct answer: $$120.83 cm^2$$

$$130.83 cm^2$$

$$140.83 cm^2$$

Q6.
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?

Correct answer: Tangent

Sine

Cosine

Lesson appears in

UnitMaths / Trigonometry

Maths

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Choosing an appropriate method for finding lengths of a triangle

Choosing an appropriate method for finding lengths of a triangle

Lesson slides

Lesson details

Key learning points

Keywords

Common misconception

Licence

Lesson video

Worksheet

Prior knowledge starter quiz

6 Questions

Q1.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.)

Q2.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.)

Q3.Would a triangle ABC with sides AB = 9cm, BC = 7.5cm, AC = 12.5cm be similar to the one shown in the diagram?

Q4.For this pair of triangles, can you determine whether they are similar without using side lengths?

Q5.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.)

Q6.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.)

Assessment exit quiz

6 Questions

Q1.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?

Q2.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. ?

Q3.If the area of square ABCD is $$25 cm^2$$, what is the length of the diagonal BD to 2 d.p. ?

Q4.A rectangle ABCD has length 6cm, and the diagonal angle ABC is 38ᵒ. What is the height of the rectangle to 2 d.p. ?

Q5.A rectangle ABCD has length 12cm, and the diagonal angle ABC is 40ᵒ. What is the area of the rectangle to 2 d.p. ?

Q6.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?

Lesson appears in

UnitMaths / Trigonometry

Maths

Q1.
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.)

Q2.
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.)

Q3.
Would a triangle ABC with sides AB = 9cm, BC = 7.5cm, AC = 12.5cm be similar to the one shown in the diagram?

Q4.
For this pair of triangles, can you determine whether they are similar without using side lengths?

Q5.
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.)

Q6.
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.)

Q1.
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?

Q2.
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. ?

Q3.
If the area of square ABCD is $$25 cm^2$$, what is the length of the diagonal BD to 2 d.p. ?

Q4.
A rectangle ABCD has length 6cm, and the diagonal angle ABC is 38ᵒ. What is the height of the rectangle to 2 d.p. ?

Q5.
A rectangle ABCD has length 12cm, and the diagonal angle ABC is 40ᵒ. What is the area of the rectangle to 2 d.p. ?

Q6.
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?