Grade 10 Maths · Trigonometry

Write trig ratios in a triangle

Name the opposite, adjacent and hypotenuse sides for an angle in a right-angled triangle and write sin, cos or tan, for example sin θ = opposite/hypotenuse.

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Grade 10 Trigonometry: Trig Ratios Sin, Cos and TanMiss Martins Maths and Science

Trigonometry Grade 10: Introduction to trigMiss Martins Maths and Science

Trigonometry | SOH CAH TOA | Sin, Cos, TanCognito

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Question 6.1.1 · March 2022 · Provincial · 2 marks

Given

cos 2 0^{\circ} = p

and

sin 1 4^{\circ} = q

6.1 Without using a calculator, calculate the value of the following in terms of

p

q

p

and

q

6.1.1

sin 2 0^{\circ}

(2)

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

More past paper questions: write trig ratios in a triangle

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3. Question 4.1.3 · November 2024 · Paper 2 · Provincial · 3 marks
In the diagram is a right-angled triangle has sides a, b and c and the $\hat{B} = 9 0^{\circ}$ .
4.1 Write down the following in terms of a, b and c.
4.1.3 If it is given that $a = 5$ and $A = 5 0^{\circ}$ calculate the numerical value of c.(3)
Show the memo (3 ticks)Memo
1. ✓
  Answer $c = \frac{5}{c o t 4 0 ^{\circ}} = \frac{5}{t a n 5 0 ^{\circ}} \approx 4, 20$
  1 mark · Calculate a side using trig
2. ✓
  S/R: size of Ĉ $\hat{C} = 18 0^{\circ} - 9 0^{\circ} - 5 0^{\circ} = 4 0^{\circ}$ (sum of $∠$ s of $Δ$ )
  1 mark · Use angle sum of a triangle
3. ✓
  Substitution into cot C $cot C = \frac{a}{c}$ | $cot 4 0^{\circ} = \frac{5}{c}$
  1 mark · Calculate a side using trig
4. Question 3.1.2 · March 2025 · Provincial · 1 mark
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:
3.1.2 Write down the trigonometric ratio that is equal to $\frac{QR}{PR}$ (1)
Show the memo (1 tick)Memo
1. ✓
  Identify ratio $sin θ$ (or $cos Q \hat{R} P$ )
  1 mark · Write trig ratios in a triangle
5. Question 3.1.1(a) · March 2024 · Provincial · 1 mark
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:
3.1.1 Write down the values of:
3.1.1(a) $tan θ$ (1)
Show the memo (1 tick)Memo
1. ✓
  Ratio $\frac{s}{q}$
  1 mark · Write trig ratios in a triangle
6. Question 3.1.1 · March 2023 · Provincial · 1 mark
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)
3.1.1 $cos θ$ (1)
Show the memo (1 tick)Memo
1. ✓
  Ratio $\frac{5}{74}$
  1 mark · Write trig ratios in a triangle

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