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

The opposite side of a right-angled triangle is the side which is opposite the marked angle.

The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle.

Scaling the right-angled triangle from the unit circle

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

Which letter represents the opposite side to the non-right angle shown in the diagram?

Using ABCD, which side would represent the opposite if we were using angle CBD?

Assuming the two triangles are similar and all measures are in cm, if length AB is 9 what is length BC? 

Assuming the two triangles are similar and all measures are in cm, if length AB is 11 what is length AC? 

Assuming the two triangles are similar and all measures are in cm, if length BC is 3.6 cm what is length AB? 

In a right triangle, if the hypotenuse is 39 cm and a second side is 15 cm, what is the area? (Use a calculator to help you.)

In a right triangle, if the hypotenuse is 125 cm and a second side is 75 cm, what is the length of the third side? (Use a calculator to help you.)

In a right triangle, if the hypotenuse is 22.5 cm and a second side is 13.5 cm, what is the perimeter? (Use a calculator to help you.)

In a right triangle, if the shortest sides are 22.5 cm and 30 cm, what is the length of the hypotenuse? (Use a calculator to help you.)

Would a right triangle ABC with side AB = 24cm, and hypotenuse AC = 30cm be similar to the one shown in the diagram?

Yes, they are not similar in this case as their angles are different.

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?

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