Sines or Cosines?

Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 18 of 37.

Before you tap anything, ask one question: do I know a side together with the angle across from it?

Yes: use the law of sines. That covers two angles and a side (AAS and ASA, after the angle sum) and two sides with an angle across from one of them (SSA). No: use the law of cosines. That covers two sides with the angle between them (SAS) and three sides (SSS).

$Triangle KLM with KL = 25, KM = 18 and 52° at K$

In triangle KLM, KL = 25, KM = 18 and K = 52°. The 52° is between the two known sides, and neither side faces a known angle: SAS. So ${n}^{2} = {25}^{2}+{18}^{2}-2\cdot 25\cdot 18\cdot \cos\left(52^{\circ}\right)$ , and n is about 19.87.

Challenge

In triangle PQR, PQ = 23 m, QR = 31 m and the angle at Q is 47°. Find PR, marked x, to two decimal places. Choose the law yourself, then press Check.

Try it yourself

$Use the figure to find x$