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S4 Maths: Trigonometric Ratios and Bearings (Paper 1 (basics))
S4 Maths: Trigonometric Ratios and Bearings (Paper 1 (basics))
Paper 1 (basics): ten questions on trigonometric ratios and bearings with answers and one-line notes.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: S4 Maths: Trigonometric Ratios and Bearings |
| Level | S4 |
02 Questions (10 items)
- FoundationIn a right-angled triangle the side opposite the angle is 3 cm, the adjacent side is 4 cm and the hypotenuse is 5 cm. Find sin of the angle.
- FoundationA right-angled triangle has opposite side 5 cm and hypotenuse 13 cm. Find sine of the angle to three decimal places.
- FoundationWhat is the value of tan 45 degrees?
- IntermediateA right-angled triangle has a hypotenuse of 10 cm and one acute angle of 30 degrees. Find the opposite side.
- IntermediateA right-angled triangle has an adjacent side of 8 cm and an angle of 60 degrees. Find the opposite side.
- IntermediateIn a 3-4-5 right-angled triangle the opposite side is 4 cm and the hypotenuse is 5 cm. Find the cosine of the angle.
- ChallengeA right-angled triangle has hypotenuse 26 cm and one leg 10 cm, with the angle facing that leg. Find the other leg and the tangent of the angle.
- ChallengeFrom a point on the ground 20 m from the foot of a tower the angle of elevation of the top is 45 degrees. Find the height of the tower.
- ChallengeA square has side 10 cm. Find the angle between a diagonal and one side.
- Error redoError clinic: a student writes sine as adjacent divided by hypotenuse and gets a wrong answer. What is the correct form?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | Sine is opposite divided by hypotenuse: 3 / 5 = 0.6. | The denominator of sine is always the hypotenuse, so the adjacent side of 4 cm is not used here. |
| 2 | Sine equals 5 / 13, which is about 0.385. | When the division does not terminate, keep three decimal places or leave it as the fraction 5 over 13. |
| 3 | tan 45 degrees equals 1. | At 45 degrees the two legs are equal, so opposite divided by adjacent is exactly 1. |
| 4 | Opposite = 10 x sin 30 = 10 x 0.5 = 5 cm. | When the hypotenuse and an angle are known, sine gives the opposite side; using cosine would give the adjacent. |
| 5 | Opposite = 8 x tan 60, which is about 13.856 cm. | With the adjacent side known, tangent is the ratio to use because its numerator is the opposite side. |
| 6 | Cosine is adjacent over hypotenuse: 3 / 5 = 0.6. | The opposite side is 4, so the remaining leg of 3 is the adjacent side that cosine needs. |
| 7 | Other leg = square root of (26 squared minus 10 squared) = 24 cm; tangent is 10 / 24, about 0.417. | Use Pythagoras first to complete the third side so that tangent has both its opposite and adjacent sides. |
| 8 | Height = 20 x tan 45 = 20 m. | An angle of elevation is measured up from the horizontal, so the horizontal distance times tangent gives the height. |
| 9 | The angle is 45 degrees, because a diagonal splits the square into two isosceles right-angled triangles. | Equal legs give a tangent of 1, and the matching angle is 45 degrees. |
| 10 | Sine is opposite over hypotenuse; adjacent over hypotenuse gives cosine instead. | The numerator is the part students mix up most, so check which side the question actually gives. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
For any trigonometric question, start by drawing the triangle, marking the right angle and labelling the three sides: the side facing the angle is the opposite, the side touching the angle beside the right angle is the adjacent, and the longest side is the hypotenuse. The three ratios differ only in the denominator: sine uses the hypotenuse, cosine uses the hypotenuse, and tangent uses the adjacent. Once the ratio is written, see which two quantities are known and pick the formula that contains only those two, leaving a single unknown. Memorise the values for 30, 45 and 60 degrees so no calculator is needed when they appear. Bearings are always measured clockwise from north: 0 is north, 90 is east, 180 is south and 270 is west, so convert an N..E statement by splitting the angle from north or from south and checking that the two parts add up to the bearing given. Finally test the answer against the triangle: the hypotenuse must be the longest side and every ratio must be less than 1.Tutor Registration →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.
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