Grade 10 Maths · Trigonometry

Calculate a side using trig

Find a missing side of a right-angled triangle using sin, cos or tan, for example with hypotenuse 10 and angle 30°, opposite = 10 sin 30° = 5.

past paper questions use it: 13 past paper questions use it
videos: 3 videos

Learn it: calculate a side using trig

Pick one and watch it, then try the questions below. Videos load only when you tap play.

Grade 10 Trigonometry Finding the length of a side vs Finding the angleMiss Martins Maths and Science

Trigonometry: Finding missing sides and anglesScience Made Simple

Now try it on a real exam question

No sign-up. Takes 3 minutes.

Question 8.1 · May/June 2025 · Paper 2 · National (DBE) · 2 marks

In the diagram, A, B and C lie in the same horizontal plane with

A B = A C

. D is directly above A such that

2 A D = BC

. Also,

A D = p

A \hat{B} C = x

and

D \hat{B} A = y

8.1 Determine AB in terms of p and y.(2)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

More past paper questions: calculate a side using trig

Work each one out first, then open the memo and check every tick.

3. Question 6.2 · November 2024 · Paper 2 · Provincial · 2 marks
An observer on the top of a cliff, 200 m above the sea level, observes the angles of depression of the two ships to be $4 5^{\circ}$ for ship A, and $3 0^{\circ}$ for ship B.
6.2 Calculate the length of BC.(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitution $tan B = \frac{D C}{BC}$ | $tan 4 5^{\circ} = \frac{200}{BC}$
  1 mark · Calculate a side using trig
2. ✓
  Answer $BC = 200$ m
  1 mark · Calculate a side using trig
4. Question 6.2.2 · September 2024 · Provincial · 4 marks
6.2 A handy man attempts to reach the roof of a hall with a ladder 5 metres in length. Unfortunately, the ladder is too short, and a new ladder will be required. Suppose that the length of the ladder needed to reach the top has to be double the distance from the foot of the ladder to the wall. Also, the angle between his current ladder and the ground will need to be equal to the angle between the two ladders.

The above situation is depicted in the diagram below.
6.2.2 If $θ = 3 0^{\circ}$ , determine what the length of the ladder should be, to get the handy man to the roof.(4)
Show the memo (3 ticks)Memo
1. ✓
  $cos 3 0^{\circ} = \frac{x}{5}$ (double tick) $cos 3 0^{\circ} = \frac{x}{5}$
  2 marks · Calculate a side using trig
2. ✓
  Value of x $x = 5 cos 3 0^{\circ} = 4, 33$ m
  1 mark · Calculate a side using trig
3. ✓
  Answer $Length = 2 x = 2 (4, 33) = 8, 66$ m
  1 mark · Calculate a side using trig
5. Question 4.1 · June 2024 · Paper 2 · Provincial · 4 marks
In the diagram below, $\hat{A} = θ$ and $A \hat{B} D = 9 0^{\circ}$ . $BC = x$ m, $\hat{C} = β$ and $B \hat{D} C = 9 0^{\circ}$ .
4.1 Show that $A B = \frac{x s i n β}{t a n θ}$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Express BD in terms of x and betaIn $Δ BC D$ :
  $sin β = \frac{B D}{x}$
  $B D = x sin β$
  2 marks · Calculate a side using trig
2. ✓
  Express AB in terms of BD and thetaIn $Δ A B D$ :
  $tan θ = \frac{B D}{A B}$
  $A B = \frac{B D}{t a n θ}$
  1 mark · Calculate a side using trig
3. ✓
  Substitute BD to prove formula $A B = \frac{x s i n β}{t a n θ}$
  1 mark · Calculate a side using trig
6. Question 3.1.2 · March 2024 · Provincial · 2 marks
A right angled triangle with sides $p$ , $q$ and $s$ and the angle $θ$ is given. (Based on diagram: $p$ = Hypotenuse, $q$ = Adjacent, $s$ = Opposite to $θ$ )
3.1 Refer to the diagram:
3.1.2 If it is given that $p = 12$ and $θ = 3 5^{\circ}$ , calculate the numerical value of $q$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Set up trig ratio $cos 3 5^{\circ} = \frac{q}{12}$
  1 mark · Calculate a side using trig
2. ✓
  Solve $q = 12 cos 3 5^{\circ} \approx 9, 83$
  1 mark · Calculate a side using trig

Free on Android

Know exactly which skill is costing you marks.

Mark past papers tick by tick in the NavyBlue app. It remembers every mark you lose, shows you the skills to fix first, and picks your next questions.

The NavyBlue app showing a learner's weak skills