Grade 10 Maths · Trigonometry

Use the theorem of Pythagoras

Use a² + b² = c² to find a missing side of a right-angled triangle (for example sides 3 and 4 give a hypotenuse of 5).

past paper questions use it: 41 past paper questions use it
videos: 3 videos

Learn it: use the theorem of pythagoras

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

Pythagoras Theorem grade 9Kevinmathscience

Grade 8 Maths: PythagorasGood Better Best Online Videos

Pythagorean Theorem: A Step-by-Step Guide | Find a Missing Side Length Using the Pythagorean TheoremMath with Mr. J

Now try it on a real exam question

No sign-up. Takes 3 minutes.

Question 4.3 · May/June 2025 · Paper 2 · National (DBE) · 3 marks

In the diagram, M is the centre of the circle having equation

(x - 3)^{2} + y^{2} = 25

E (- 1; 3)

and T are points on the circle.

EC is a tangent to the circle at E and cuts the x-axis at D.

E D = \frac{15}{4}

units. MT is produced to meet the tangent at

C (- 7; p)

4.3 Calculate the length of DM.(3)

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

More past paper questions: use the theorem of pythagoras

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

3. Question 3.1.1(a) · March 2025 · Provincial · 2 marks
In the diagram, $△ PQR$ is a right-angled triangle, $\hat{Q} = 9 0^{\circ}$ , $\hat{P} = θ$ , $PQ = 5$ and $PR = 13$ units.
3.1 Refer to the diagram:
3.1.1 Determine the numerical value of:
3.1.1(a) QR(2)
Show the memo (2 ticks)Memo
1. ✓
  Pythagoras $Q R^{2} = P R^{2} - P Q^{2}$
  $Q R^{2} = 1 3^{2} - 5^{2} = 169 - 25 = 144$
  1 mark · Use the theorem of Pythagoras
2. ✓
  Answer $QR = 12$
  1 mark · Use the theorem of Pythagoras
4. Question 5.1.1 · May/June 2025 · Paper 2 · National (DBE) · 3 marks
5.1 If $cos θ = - \frac{5}{13}$ where $18 0^{\circ} < θ < 36 0^{\circ}$ , determine, without using a calculator, the value of:
5.1.1 $sin^{2} θ$ (3)
Show the memo (2 ticks)Memo
1. ✓
  METHOD 1: Calculate the y-value using Pythagoras $cos θ = \frac{x}{r} = \frac{- 5}{13}$
  $x = - 5$ , $r = 13$
  $y^{2} = r^{2} - x^{2}$
  $y^{2} = 1 3^{2} - (- 5)^{2}$
  $y^{2} = 169 - 25 = 144$
  $y = \pm 12$
  Since $18 0^{\circ} < θ < 36 0^{\circ}$ and $cos θ$ is negative, $θ$ is in the 3rd quadrant. Therefore, $y = - 12$ .
  1 mark · Use the theorem of Pythagoras
2. ✓
  Calculate the squared sine ratio $sin^{2} θ = (\frac{y}{r})^{2}$
  $sin^{2} θ = (- \frac{12}{13})^{2}$
  $sin^{2} θ = \frac{144}{169}$
  2 marks · Find trig ratios from a sketch
5. Question 2.2.1 · June 2024 · Paper 2 · Provincial · 2 marks
2.2 In the diagram below, point $P (- 2; - 1)$ lies in the third quadrant. $OP = r$ cm. The axes intersect at O, which represents the origin.
2.2.1 Calculate the length of OP.(2)
Show the memo (1 tick)Memo
1. ✓
  Use Pythagoras theorem $r^{2} = (- 2)^{2} + (- 1)^{2}$
  $r = 5$
  2 marks · Use the theorem of Pythagoras
6. Question 2.3.3 · June 2024 · Paper 2 · Provincial · 2 marks
2.3 Given: $k sin β = - 5$ and $k cos β - 1 = 0$ where $k > 0$ .
2.3.3 Hence or otherwise, determine the numerical value of $k$ without the use of a calculator.(2)
Show the memo (2 ticks)Memo
1. ✓
  Use Pythagoras $x^{2} + y^{2} = r^{2}$ (or identify sides)
  $x = 1, y = - 5, r = k$
  $(1)^{2} + (- 5)^{2} = k^{2}$
  1 mark · Use the theorem of Pythagoras
2. ✓
  Solve for k $1 + 25 = k^{2} ⟹ k = 26$ (since $k > 0$ )
  1 mark · Use the theorem of Pythagoras

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