AQA•GCSE•Mathematics•Geometry & Measures
Trigonometric ratios (SOHCAHTOA)
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EasyQuestion 1
[2 marks]In a right-angled triangle, the angle is 35° and the hypotenuse is 12 cm. Find the length of the opposite side.
Solution for Question 1
MediumQuestion 2
[3 marks]In a right-angled triangle, the opposite side is 8 cm and the adjacent side is 15 cm. Find the angle θ.
Solution for Question 2
HardQuestion 3
[4 marks]A ladder 6m long leans against a wall. The foot of the ladder is 2m from the wall. Calculate:
(a) The angle the ladder makes with the ground
(b) How high up the wall the ladder reaches
Solution for Question 3
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Trigonometry uses ratios of sides in right-angled triangles to find missing angles and lengths. SOHCAHTOA helps remember the three ratios.
**The Three Ratios:**
- **SOH:** sin(θ) = Opposite / Hypotenuse
- **CAH:** cos(θ) = Adjacent / Hypotenuse
- **TOA:** tan(θ) = Opposite / Adjacent
**Identifying the Sides:**
- Hypotenuse: Longest side, opposite the right angle
- Opposite: Side opposite to the angle you are working with
- Adjacent: Side next to the angle (not the hypotenuse)
**Finding a Side:**
1. Label the sides O, A, H relative to the given angle
2. Identify which ratio involves your known and unknown sides
3. Substitute and solve
**Finding an Angle:**
1. Calculate the ratio using the two known sides
2. Use inverse function: θ = sin⁻¹, cos⁻¹, or tan⁻¹
**Exam Tips:**
- Check calculator is in DEGREE mode
- Draw and label the triangle
- SOHCAHTOA only works in right-angled triangles
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