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IB Mathematics: Applications and Interpretation HL · 12.10: Geometry & Trigonometry · 12.10.13

Name Date

The sine rule: the ambiguous case Problem set B

Sketch each triangle. Give angles to 1 decimal place or 3 significant figures, and check the angle sum for a second solution.

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 ABC has angle A = 58°, side BC = 17.3 cm and side AC = 13.6 cm. Find angle B.

    17.3 cm13.6 cm58°ABC

  2. A triangle ABC has angle A = 105°, BC = 14.8 cm and AC = 8.9 cm. Find angle B.

    14.8 cm8.9 cm105°ABC

  3. A triangle ABC has angle A = 36°, BC = 7.9 cm and AC = 11.6 cm. Find the two possible values of angle B.

    7.9 cm11.6 cm7.9 cm36°AB′BC

  4. A triangle ABC has angle A = 52°, BC = 10.4 cm and AC = 12.6 cm. Angle B can have two values. Find

    1. (a) both possible values of angle B
    2. (b) the angle C in each case

  5. A triangle ABC has angle A = 40° and AC = 12 cm. How many different triangles are there when BC is

    1. (a) a = 6 cm
    2. (b) a = 10 cm
    3. (c) a = 14 cm
    4. (d) a = 12 cm

In context

  1. A walker leaves a hut H and walks 12 km to a summit S. A lake L is 9.5 km from the summit and angle LHS = 35°. Find

    9.5 km12 km9.5 km35°HL′LS
    1. (a) the two possible sizes of angle HLS
    2. (b) the two possible distances HL

  2. A pilot at P sees a control tower T and a radio mast R. PR = 29.5 km, TP = 21.7 km and angle PTR = 71°. Find angle PRT.

    29.5 km21.7 km71°θTRP

Stretch

  1. A joiner makes a triangular brace ABC with AB = 18 cm and angle A = 40°. The side BC has length x cm. Find the values of x for which two different braces can be made.

  2. A triangle ABC has angle A = 34°, BC = 8.4 cm and AC = 14.2 cm. There are two possible triangles. Find

    1. (a) both possible values of angle B
    2. (b) the area of each triangle

jmaths.xyz · AI HL · 12.10.13 The sine rule: the ambiguous case