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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 B

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

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. In triangle DEF, angle D = 44°, angle E = 63° and EF = 9.6 cm. Find the length of FD.

    9.6 cmx44°63°DEF

  2. In triangle XYZ, angle X = 58°, YZ = 12.3 cm and ZX = 9.4 cm. Find angle Y, which is acute.

    12.3 cm9.4 cm58°θXYZ

  3. In triangle KLM, angle L = 49°, MK = 15.8 cm and KL = 12.2 cm.

    15.8 cm12.2 cm49°KLM
    1. (a) Find angle M, which is acute.
    2. (b) Find angle K.

  4. In triangle DEF, FD = 8.6 cm, DE = 5.3 cm and angle D = 125°. Find the length of EF.

    x8.6 cm5.3 cm125°DEF

  5. In triangle PQR, QR = 6.9 cm, RP = 9.3 cm and PQ = 12.0 cm. Find the largest angle.

    6.9 cm9.3 cm12.0 cmθPQR

  6. The diagram shows triangle XYZ. The perpendicular from Z meets XY at S, and ZS = h. The side opposite X is x and the side opposite Y is y. Show that \(\frac{x}{\sin X}=\frac{y}{\sin Y}\).

    xyhXYXYZS

In context

  1. Two lighthouses P and Q stand 250 m apart on a straight pier. A boat R is out at sea. Angle RPQ = 54° and angle RQP = 78°. Find the distance PR.

    x250 m54°78°PQR

  2. Two hikers leave a camp C. One walks 6.4 km to a hut H and the other walks 9.1 km to a lake K. The angle HCK is 105°. Find the distance HK.

    x9.1 km6.4 km105°CHK

  3. A triangular park has sides of 64 m, 96 m and 125 m. Find the largest angle of the park.

    64 m96 m125 mθDEF

Stretch

  1. In triangle DEF, DE = 11.6 cm, DF = 15.2 cm and angle D = 37°.

    x15.2 cm11.6 cm37°DEF
    1. (a) Find EF.
    2. (b) Find angle EFD.

  2. A flower bed PQRS has sides PQ = 7.5 m, QR = 5.8 m, RS = 8.3 m and SP = 6.6 m. Angle PQR = 75°.

    7.5 m5.8 m8.3 m6.6 m75°θPQRS
    1. (a) Find the length of PR.
    2. (b) Find angle PSR.

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