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Right-angled Triangles

We estimate MS1-12-RT is worth about 12 marks out of 100 under the new Mathematics Standard 1 syllabus. Practise 12 exam-style questions (multiple choice, numerical answer, multi-part, short answer) with instant marking and a worked solution for every question.

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Topic notes

Pythagoras' theorem and the sine, cosine and tangent ratios in right-angled triangles, angles in degrees and minutes, angles of elevation and depression, and compass and true bearings, with worked practical examples.

  1. 1What you need to know
  2. 2Pythagoras' theorem
  3. 3The trigonometric ratios
  4. 4Angles of elevation and depression
  5. 5Bearings
  6. 6Common mistakes
  7. 7Exam tips
  8. 8Links to other topics
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Example questions

Example 1 · 1 mark · multiple choice

A ramp is 12 m long and makes an angle of 35° with the horizontal ground. How high does the top of the ramp rise above the ground, correct to 2 decimal places?

  1. A20.92 m
  2. B9.83 m
  3. C6.88 m
  4. D8.40 m

Example 2 · 1 mark · multiple choice

In right-angled triangle ABC, the right angle is at B. AB = 12 cm and BC = 7 cm. What is the size of angle A, to the nearest minute?

  1. A
  2. B
  3. C
  4. D

Example 3 · 4 marks · multi-part

A boat sails from port A for 24 km on a true bearing of 060° to point B. It then turns and sails 18 km on a true bearing of 150° to point C.

From B, the bearing back to A is and the bearing to C is . Since angle ABC is a right angle.

Answers and worked solutions appear when you practise these questions.

Other Mathematics Standard 1 topics