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 $$\cos(30^\circ)$$?

Starter Quiz