Checking and securing understanding of sine ratio problems | Maths

Starter quiz

Two shapes are ______ if the only difference between them is their size. Their side lengths are in the same proportions.

congruent

similar ✓

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

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

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

'41' ✓
$What is the approximate value of <Math>\sin(60^\circ)</Math>?$

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

'0.87' ✓
$What is the approximate value of <Math>\sin(30^\circ)</Math>?$

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

'0.5' ✓

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

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

'6 cm' ✓
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?

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

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

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

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

$\text{hyp}=\frac{\text{opp}}{\sin(\theta)}$ ✓
Which of the following equations are correct when finding the angle $n^\circ$ in the equation: $\sin(n^\circ)=0.38$ ?

$n=\frac{0.38}{\sin()}$

$n=\sin(0.38)$

$n=\arcsin(0.38)$ ✓

$n=\sin^{-1}(0.38)$ ✓
Which of these is correct for this triangle?

$\sin(x)=\frac{3}{5}$

$\sin(x)=\frac{5}{3}$

$\sin(x)=\frac{4}{5}$ ✓

$\sin(x)=\frac{5}{4}$

$\sin(x)=\frac{4}{3}$
Calculate the length of $x$ to 2 decimal places.

'7.06 cm' ✓

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The sine ratio involves the hypotenuse, opposite and the angle
If you know the length of the hypotenuse and the size of the angle, you can use the sine ratio
If you know the length of the opposite and the size of the angle, you can use the sine ratio
If you know the length of the hypotenuse and opposite, you can use the sine ratio

Incorrectly rearranging the sine formula.

A ratio table can be helpful to see the relationship between the sides and therefore how to rearrange.

Hypotenuse - The hypotenuse is the side of a right-angled triangle which is opposite the right angle.
Opposite - The opposite side of a right-angled triangle is the side which is opposite the marked angle.
Trigonometric functions - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle for a given angle.
Sine function - The sine of an angle (sin(θ°)) is the y-coordinate of point P on the triangle formed inside the unit circle.