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If none of the angles of a triangle is a right angle, the triangle is called oblique. To solve an oblique triangle means to find the lengths of its sides and the measurements of its angles. A S A ASA S A A SAA CASE 1: ASA or SAA S A S CASE 2: SSA S A S CASE 3: SAS S S S CASE 4: SSS Name the case 5 47o 7 (1)SSS (2)SAS (3)SSA (4)ASA Theorem Law of Sines For a triangle with sides a , b, c and opposite angles , , , respectively, sin sin sin a b c Proof (one case) a b h opp h sin , so h b sin hyp b opp h sin , so h a sin hyp a h b sin a sin sin sin a b Solve the triangle: = 30 , 70 , a 5 (SAA) 180 30 b 30 70 180 80 c sin 30 sin 70 sin 30 sin 80 70 5 b 5 c 5 5 sin 70 5 sin 80 b 9.40 c 9.85 sin 30 sin 30 Solve the triangle: c 5, b 3, 50 (SSA) sin 50 sin 3 5 5 sin 50 sin 3 3 5 50 a sin 128 . No triangle with the given measurements! Which numbers not allowed in LOS problem for sin α? (1) -0.7 (2) 0 (3) 0.7 (4) 1.4