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IB Mathematics: Applications and Interpretation HL · 12.10: Geometry & Trigonometry · 12.10.2

Name Date

Sine rule and cosine rule Problem set A

Sketch a diagram if there is none. Say which rule you use. Give angles and lengths to 3 significant figures, with units.

Difficulty: first skills applying them stretch

Skills

  1. In triangle ABC, angle A = 52°, angle B = 71° and BC = 8.3 cm. Find the length of CA.

    8.3 cmx52°71°ABC

  2. In triangle PQR, angle P = 67°, QR = 14.5 cm and RP = 10.6 cm. Find angle Q, which is acute.

    14.5 cm10.6 cm67°θPQR

  3. In triangle ABC, angle B = 68°, CA = 12.1 cm and AB = 8.7 cm.

    12.1 cm8.7 cm68°ABC
    1. (a) Find angle C, which is acute.
    2. (b) Find angle A.

  4. In triangle ABC, CA = 9.7 cm, AB = 6.4 cm and angle A = 108°. Find the length of BC.

    x9.7 cm6.4 cm108°ABC

  5. In triangle ABC, BC = 8.2 cm, CA = 10.5 cm and AB = 13.1 cm. Find the largest angle.

    8.2 cm10.5 cm13.1 cmθABC

  6. The diagram shows triangle PQR. The perpendicular from R meets PQ at S, and RS = h. The side opposite P is p and the side opposite Q is q. Show that \(\frac{p}{\sin P}=\frac{q}{\sin Q}\).

    pqhPQPQRS

In context

  1. Two surveyors, A and B, stand 120 m apart on one bank of a lake. They look at a tree C on the other bank. Angle CAB = 62° and angle CBA = 71°. Find the distance AC.

    x120 m62°71°ABC

  2. Two ships leave port P at the same time. Ship A sails 18 km on one course and ship B sails 25 km on another. The angle between the two courses is 52°. Find the distance between the ships.

    x25 km18 km52°PAB

  3. A triangular field has sides of 85 m, 112 m and 140 m. Find the largest angle of the field.

    85 m112 m140 mθABC

Stretch

  1. In triangle ABC, AB = 9.4 cm, AC = 12.7 cm and angle A = 41°.

    x12.7 cm9.4 cm41°ABC
    1. (a) Find BC.
    2. (b) Find angle BCA.

  2. In the quadrilateral ABCD, AB = 6.2 cm, BC = 8.4 cm, CD = 9.0 cm, DA = 7.1 cm and angle ABC = 70°.

    6.2 cm8.4 cm9.0 cm7.1 cm70°θABCD
    1. (a) Find the length of AC.
    2. (b) Find angle ADC.

jmaths.xyz · AI HL · 12.10.2 Sine rule and cosine rule