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

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

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

The cosine of an angle (cos(θ°)) is the x-coordinate of point P on the triangle formed inside the unit circle.

Checking and securing understanding of cosine problems

Maths

In this unit, pupils have explored the trigonometric ratios for right-angled triangles in a variety of situations. In the future unit, pupils explore what can be done when we have a triangle that is not right-angled.

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

Right-angled trigonometry

Work out the length of $$x$$, given that these two triangles are similar.

$$\text{hyp}=\frac{\cos(\theta)}{\text{adj}}$$

$$\theta=\arccos\left(\frac{\text{adj}}{\text{hyp}}\right)$$

$$\text{hyp}\times\cos(\theta)=\text{adj}$$

$$\cos(\theta)=\frac{\text{hyp}}{\text{adj}}$$

$$\text{hyp}=\frac{\text{adj}}{\cos(\theta)}$$

For a right-angled triangle, the cosine ratio is $$\cos(\theta)=\frac{\text{adj}}{\text{hyp}}$$, where $$\theta$$ is the angle in degrees. Which of these are equivalent forms?

Which of the following equations are correct when finding the angle $$n^\circ$$ in the equation: $$\cos(n^\circ)=0.57$$?

Which of these is correct for this triangle?

Calculate the length of $$x$$ to 2 decimal places.

Two shapes are similar if the only difference between them is their {{}}. Their side lengths are in the same proportions. 

Triangle ABC and triangle DEF are similar. What is the length of side $$x$$?

The two triangles are similar. What is the size of the angle marked $$x$$?

What is the approximate value of $$\cos(60^\circ)$$?

What is the approximate value of $$\cos(30^\circ)$$?

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

Checking and securing understanding of cosine problems

Lesson outcome

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