Checking and securing understanding of tangent ratio problems | Maths

Starter quiz

$Match the names of the sides, relative to the angle <Math>\theta</Math>.$

Match the names of the sides, relative to the angle $\theta$ .

a

⇔

opposite ✓

b

⇔

adjacent ✓

c

⇔

hypotenuse ✓
The two triangles are similar. What is the length of $x$ ?

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

'16 cm' ✓
Work out the value of $x$ to 3 significant figures.

'4.99' ✓
Work out the value of $x$ to 1 decimal place.

'8.6' ✓
Work out the length of $x$ , to 1 decimal place.

'12.7 cm' ✓

Exit quiz

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

$\tan(\theta)=\frac{\text{adj}}{\text{opp}}$

$\text{adj}\times\tan(\theta)=\text{opp}$ ✓

$\text{adj}=\frac{\tan(\theta)}{\text{opp}}$

$\theta=\arctan\left(\frac{\text{opp}}{\text{adj}}\right)$ ✓

$\text{adj}=\frac{\text{opp}}{\tan(\theta)}$ ✓
Work out the length of $x$ , to 1 decimal place.

'11.7 cm' ✓
Work out the length of $x$ , to 1 decimal place.

'10.1 cm' ✓
$Using the table of values, what is the value of <Math>\theta</Math>?$

Using the table of values, what is the value of $\theta$ ?

0

5

10

15 ✓

20
Match the variables to their values.

opposite

⇔

33 ✓

adjacent

⇔

48 ✓

theta

⇔

34.50852299 ✓
$Work out the value of <Math>\theta</Math>, to the nearest degree.$

Work out the value of $\theta$ , to the nearest degree.

'42' ✓

Worksheet

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Lesson Details

Key learning points

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

Common misconception

Pupils may confuse the opposite and adjacent sides.

The orientation of the right-angled triangle is not important. Identifying the known angle is what determines which is is the opposite and which is the adjacent.

Keywords

Trigonometric functions - Trigonometric functions are commonly defined as ratios of two sides of a right-angled triangle containing the angle.
Tangent function - The tangent of an angle (tan(θ°)) is the y-coordinate of point Q of the triangle which extends from the unit circle.
Adjacent - The adjacent side of a right-angled triangle is the side which is next to both the right angle and the marked angle.
Opposite - The opposite side of a right-angled triangle is the side which is opposite the marked angle.