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

Choosing an appropriate method for finding lengths of a triangle

Maths

In this unit, pupils were introduced to the trigonometric ratios and developed the skills to ascertain which ratio would be appropriate for a given problem. In the future unit, pupils are introduced to a variety of situations where this knowledge is required, such as 3-D problems and elevation/depression.

In the prior unit, pupils continued to build on their understanding of congruence and similarity with right-angled triangles. In this unit, similarity is used to extend a right-angled triangle in the unit circle to any other right-angled triangle.

Trigonometry

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?

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. ?

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

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

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

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?

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.)

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.)

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

Yes, because their three angles correspond.

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

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

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.)

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.)

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