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.

Checking and securing understanding of sine ratio 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.

$$\sin(\theta)=\frac{\text{hyp}}{\text{opp}}$$

$$\text{hyp}\times\sin(\theta)=\text{opp}$$

$$\text{hyp}=\frac{\sin(\theta)}{\text{opp}}$$

$$\theta=\arcsin\left(\frac{\text{opp}}{\text{hyp}}\right)$$

$$\text{hyp}=\frac{\text{opp}}{\sin(\theta)}$$

For a right-angled triangle, the sine ratio is $$\sin(\theta)=\frac{\text{opp}}{\text{hyp}}$$, 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: $$\sin(n^\circ)=0.38$$?

Which of these is correct for this triangle?

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

Two shapes are {{}} if the only difference between them is their size. 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 $$\sin(60^\circ)$$?

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

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