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

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

Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.

The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.

Using the sine ratio

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

Using triangle ABC, if θ = 35ᵒ and BC = 5 cm, what is the length of the hypotenuse AB to 1 d.p. ? 

What value of $$x$$ will produce the same result for cos($$x$$) and sin(30ᵒ)?

Using triangle ABC, if θ = 40ᵒ and BC = 4.8 cm, what is the length of the hypotenuse AB to 1 d.p. ? 

What value of $$y$$ will produce the same result for sin($$y$$) and cos(26ᵒ)?

Using triangle ABC, if θ = 50ᵒ and AB = 12 cm, what is the length of side BC to 1 d.p. ? 

Using triangle ABC, if θ = 45ᵒ and AB = 18 cm, what is the length of side BC to 1 d.p. ? 

In a right triangle, if the hypotenuse is 15 cm and a second side is 9 cm, what is the perimeter? (Use a calculator to help you.)

In a right triangle, if the hypotenuse is 25 cm and a second side is 15 cm, what is the area? (Use a calculator to help you.)

Which of these is a rearrangement of $$tan(θ)=\frac{opp}{adj}$$

In a right triangle, if you are provided with θ and the hypotenuse, which function would you use to find the opposite side? 

In a right triangle, if θ = 35ᵒ and the opposite side is 7 cm, what is the length of the hypotenuse to the nearest whole number? 

This lesson will be removed by end of Summer Term 2025.

Using the sine ratio

Lesson outcome

This lesson will be removed by end of Summer Term 2025.