Grade 10 Maths · Trigonometry

Calculate an angle from a ratio

Find an angle from a trig ratio using the inverse button, for example if tan θ = 1,5 then θ ≈ 56,3°.

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Trig Triangles Grade 10: Find angleKevinmathscience

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

Inverse Trig Ratios Solving for AnglesMario's Math Tutoring

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Question 8.3 · 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

8.3 If

x = 6 0^{\circ}

, calculate the size of 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 an angle from a ratio

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3. Question 6.2.1 · September 2024 · Provincial · 3 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.
6.2.1 Calculate the value of $θ$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Set up trigonometric ratio $cos 2 θ = \frac{x}{2 x} = \frac{1}{2}$
  1 mark · Calculate an angle from a ratio
2. ✓
  Solve for 2theta $2 θ = 6 0^{\circ}$
  1 mark · Calculate an angle from a ratio
3. ✓
  Answer $θ = 3 0^{\circ}$
  1 mark · Calculate an angle from a ratio
4. Question 4.1.1 · March 2023 · Provincial · 2 marks
4.1 Solve for x where $0^{\circ} \leq x \leq 9 0^{\circ}$ , in each of the following equations. Give your answer correct to TWO decimal places.
4.1.1 $tan 3 x = 5, 75$ (2)
Show the memo (2 ticks)Memo
1. ✓
  Arctan $3 x = tan^{- 1} (5, 75) = 80, 1 3^{\circ}$
  1 mark · Calculate an angle from a ratio
2. ✓
  Solve x $x = 26, 7 1^{\circ}$
  1 mark · Calculate an angle from a ratio
5. Question 3.1.4 · March 2023 · Provincial · 2 marks
In $Δ A BC$ , $\hat{C} = 9 0^{\circ}$ and $\hat{B} = θ$ , $A C = 7$ units, $BC = 5$ units and $A B = 74$ units.
3.1 Use the diagram above to write down the value of: (Leave your answer in surd form)
3.1.4 Hence or otherwise, determine the size of $θ$ (correct to TWO decimal places).(2)
Show the memo (1 tick)Memo
1. ✓
  Answer (double tick) $cos θ = \frac{5}{74}$
  $θ = 54, 4 6^{\circ}$
  2 marks · Calculate an angle from a ratio
6. Question 4.4 · November 2024 · Paper 2 · Provincial · 3 marks
In the diagram is a right-angled triangle has sides a, b and c and the $\hat{B} = 9 0^{\circ}$ .
4.4 Solve for x, correct to two decimal places: $3 + sec x = 5$ and $0^{\circ} \leq x \leq 9 0^{\circ}$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Isolate sec x $sec x = 2$
  1 mark · Solve a linear equation
2. ✓
  Convert to cos x $cos x = \frac{1}{2}$
  1 mark · Use cosec, sec and cot
3. ✓
  Solve for x $x = 6 0^{\circ}$
  1 mark · Calculate an angle from a ratio

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