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Cambridge IGCSE Mathematics practice

exam practice - Understand and apply the sine, cosine, and tangent ratios for acute angles in right-angled triangles, with angles provided in degrees and answers expressed in degrees to one decimal place. Solve two-dimensional problems using Pythagoras' theorem and trigonometry, which may involve bearings. Recognize that the shortest distance from a point to a line is the perpendicular distance. Perform calculations related to angles of elevation and depression. - Right-angled triangles

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2

Paper

3

Marks

Topic

Right-angled triangles

Exam-style question

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Paper 2Core or Extended Mathematics3 marks

A surveyor measures the angle of elevation from a point on the ground to the top of a tower as 35°. The distance from the surveyor to the base of the tower is 50 m.

Diagram Description

Tower and Surveyor

A right-angled triangle is formed with the tower as the vertical side, the ground distance as the horizontal side, and the line of sight as the hypotenuse. The angle of elevation is 35° at the surveyor's point.

  1. a

    Calculate the height of the tower to one decimal place.

    Aim for approximately 3 distinct marking points.

    [3]

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Maths method check

  • Topic focus: Right-angled triangles.
  • Question style: structured_mathematics.
  • Reasoning demand: reasoning.
  • Check the operation, notation, units, and final answer form against the question before moving on.

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Paper 2 structured question: Right-angled triangles

Paper 2Core or Extended Mathematics4 marks

Description

Boat and Shoreline

The lighthouse is 60 m west of the shoreline. The boat is 80 m from the lighthouse on a bearing of 120°. Find the shortest distance from the boat to the shoreline.

  1. a

    Calculate the shortest distance from the boat to the shoreline, correct to one decimal place.

    Aim for approximately 4 distinct marking points.

    [4]