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SOHCAHTOA (trigonometry) practice questions with answers

Foundation and Higher · Grade 5 · Calculator

A second set of SOHCAHTOA (trigonometry) questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

Opposite 8 and hypotenuse 17. Find the sine of the angle.

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Answer: 8/17

  1. Sine is opposite / hypotenuse.
  2. Ratio is 8/17.
  • Method (1): Sine is opposite / hypotenuse.
  • Accuracy (1): Ratio is 8/17.

Question 2 Easy

Opposite 9 and hypotenuse 15. Find the sine of the angle.

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Answer: 3/5

  1. Sine is opposite / hypotenuse: 9/15.
  2. Simplify fraction: 3/5.
  • Method (1): Sine is opposite / hypotenuse: 9/15.
  • Accuracy (1): Simplify fraction: 3/5.

Question 3 Medium

Opposite 8 and adjacent 15. Find the tangent of the angle.

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Answer: 8/15

  1. Tangent is opposite / adjacent.
  2. Ratio is 8/15.
  • Method (1): Tangent is opposite / adjacent.
  • Accuracy (1): Ratio is 8/15.

Question 4 Medium

Opposite 7 and adjacent 24. Find the tangent of the angle.

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Answer: 7/24

  1. Tangent is opposite / adjacent.
  2. Ratio is 7/24.
  • Method (1): Tangent is opposite / adjacent.
  • Accuracy (1): Ratio is 7/24.

Question 5 Hard

Angle 45 degrees and hypotenuse 8. Find the opposite side.

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Answer: 4√2

  1. sin 45 = √2/2.
  2. Opposite = 8 × (√2/2) = 4√2.
  • Method (1): sin 45 = √2/2.
  • Accuracy (1): Opposite = 8 × (√2/2) = 4√2.

Question 6 Hard

Angle 45 degrees and hypotenuse 6. Find the opposite side.

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Answer: 3√2

  1. sin 45 = √2/2.
  2. Opposite = 6 × (√2/2) = 3√2.
  • Method (1): sin 45 = √2/2.
  • Accuracy (1): Opposite = 6 × (√2/2) = 3√2.

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

Angle 30 degrees and hypotenuse 12. Find the opposite side.

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Answer: 6

  1. Formula: opposite = hypotenuse × sin 30.
  2. sin 30 = 1/2, so opposite = 12 × (1/2) = 6.
  • Method (1): Uses opposite = 12 × sin 30° with sin 30° = 1/2
  • Accuracy (1): 6

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

What does SOH represent in SOH CAH TOA?

  1. sin θ = Opposite / Hypotenuse
  2. sin θ = Adjacent / Hypotenuse
  3. sin θ = Hypotenuse / Opposite
Show answer

sin θ = Opposite / Hypotenuse SOH: Sine is Opposite over Hypotenuse.

Check 2

What does CAH represent in SOH CAH TOA?

  1. cos θ = Adjacent / Hypotenuse
  2. cos θ = Opposite / Hypotenuse
  3. cos θ = Adjacent / Opposite
Show answer

cos θ = Adjacent / Hypotenuse CAH: Cosine is Adjacent over Hypotenuse.

Check 3

What does TOA represent in SOH CAH TOA?

  1. tan θ = Opposite / Adjacent
  2. tan θ = Adjacent / Opposite
  3. tan θ = Opposite / Hypotenuse
Show answer

tan θ = Opposite / Adjacent TOA: Tangent is Opposite over Adjacent.

Check 4

In a triangle with opposite 3 and hypotenuse 5, what is sin θ?

  1. 3/5
  2. 4/5
  3. 3/4
Show answer

3/5 sin θ = Opp / Hyp = 3/5.

Check 5

In a triangle with adjacent 4 and hypotenuse 5, what is cos θ?

  1. 4/5
  2. 3/5
  3. 3/4
Show answer

4/5 cos θ = Adj / Hyp = 4/5.

Check 6

In a triangle with opposite 3 and adjacent 4, what is tan θ?

  1. 3/4
  2. 3/5
  3. 4/3
Show answer

3/4 tan θ = Opp / Adj = 3/4.

Check 7

In SOHCAHTOA, what is the exact value of sin 30°?

  1. 1/2
  2. √3/2
  3. √2/2
Show answer

1/2 sin 30° = 1/2.

Check 8

If angle is 30° and hypotenuse is 10, what is the opposite side?

  1. 5
  2. 10
  3. 5√3
Show answer

5 Opp = 10 × sin 30° = 10 × 0.5 = 5.

Check 9

If angle is 30° and hypotenuse is 6, what is the opposite side?

  1. 3
  2. 6
  3. 3√3
Show answer

3 Opp = 6 × 0.5 = 3.

Check 10

In SOHCAHTOA, what is the exact value of sin 45°?

  1. √2/2
  2. 1/2
  3. √3/2
Show answer

√2/2 sin 45° = √2/2 (or 1/√2).

Check 11

If angle is 45° and hypotenuse is 10, what is the opposite side?

  1. 5√2
  2. 5
  3. 10√2
Show answer

5√2 Opp = 10 × (√2/2) = 5√2.

Check 12

If angle is 45° and hypotenuse is 6, what is the opposite side?

  1. 3√2
  2. 3
  3. 6√2
Show answer

3√2 Opp = 6 × (√2/2) = 3√2.

Check 13

In a right triangle with opposite 5 and hypotenuse 13, what is sin θ?

  1. 5/13
  2. 12/13
  3. 5/12
Show answer

5/13 sin θ = 5/13.

Check 14

In a right triangle with opposite 8 and adjacent 15, what is tan θ?

  1. 8/15
  2. 15/8
  3. 8/17
Show answer

8/15 tan θ = 8/15.

Check 15

Which side of a right-angled triangle is always opposite the 90° angle?

  1. The hypotenuse
  2. The adjacent side
  3. The opposite side
Show answer

The hypotenuse The hypotenuse is the longest side, opposite the right angle.

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