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IB Mathematics: Applications and Interpretation SL · 12.10: Geometry & Trigonometry · 12.10.1

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Right-angled trigonometry and angles between lines Problem set B

Sketch first. Give angles to 3 significant figures, and lengths to 3 significant figures with units. Use degrees on the calculator.

Each question matches the question with the same number in set A. Do the ones you got wrong there.

Difficulty: first skills applying them stretch

Skills

  1. Triangle EFG has a right angle at F, EF = 7.2 cm and EG = 11.4 cm. Find angle FEG.

    11.4 cm7.2 cmθFEG

  2. Triangle EFG has a right angle at F, angle E = 27° and EG = 14.2 cm. Find the length of FG.

    14.2 cmx27°FEG

  3. Find the angle between the line y = 0.65x and the positive x-axis.

  4. Find the acute angle between the y-axis and each line.

    1. (a) y = 6x;
    2. (b) y = −0.8x.

  5. Find the acute angle between the lines y = 7x and y = 2.5x.

  6. Find the acute angle between the lines y = 2.5x and y = −1.5x.

  7. Find the acute angle between the lines y = 5x + 2 and y = −2x + 1.

In context

  1. A ramp 3.6 m long rises 1.0 m from level ground to a platform. The diagram shows the ramp GT, the height ET and the ground GE.

    3.6 m1.0 mθEGT
    1. (a) Find the angle θ the ramp makes with the ground.
    2. (b) A second ramp, 3.2 m long, makes an angle of 12° with the ground. How high does it rise?

  2. Two straight cycle tracks on a plan, with distances in metres, are modelled by the lines y = 1.2x + 2 and y = −0.7x + 11. Find the acute angle at which the tracks cross.

Stretch

  1. A triangle OBC is formed by the x-axis and the lines y = 1.5x and y = −2x + 10.5, where O is the origin, B is on the x-axis and C is where the two lines meet. Find the three angles of the triangle.

    OBC

jmaths.xyz · AI SL · 12.10.1 Right-angled trigonometry and angles between lines