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

Name Date

Right-angled trigonometry and angles between lines Problem set A

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

Difficulty: first skills applying them stretch

Skills

  1. Triangle PQR has a right angle at Q, PQ = 5.6 cm and QR = 9.3 cm. Find angle QPR.

    9.3 cm5.6 cmθQPR

  2. Triangle LMN has a right angle at L, angle M = 38° and LM = 7.5 cm. Find the length of LN.

    x7.5 cm38°LMN

  3. Find the angle between the line y = 1.8x and the positive x-axis.

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

    1. (a) y = 4x;
    2. (b) y = −1.5x.

  5. Find the acute angle between the lines y = 4x and y = 1.2x.

  6. Find the acute angle between the lines y = 4x and y = −0.5x.

  7. Find the acute angle between the lines y = 3x − 4 and y = −0.4x + 2.

In context

  1. A ladder 5.4 m long leans against a vertical wall. Its foot is on level ground 1.9 m from the wall. The diagram shows the ladder FT, the wall WT and the ground WF.

    5.4 m1.9 mθWFT
    1. (a) Find the angle θ the ladder makes with the ground.
    2. (b) A second ladder, 4.8 m long, makes an angle of 66° with the ground. How high up the wall does it reach?

  2. On a map, with distances in km, two straight roads are modelled by the lines y = 0.8x + 1 and y = −1.6x + 7. Find the acute angle at which the roads cross.

Stretch

  1. A triangle OBC is formed by the x-axis and the lines y = 2.5x and y = −x + 7, 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