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Ambiguous Case of the Sine Rule Non Right-Angled Triangle Trigonometry By the end of this lesson you will be able to explain/calculate the following: 1. The Ambiguous Case of the Sine Rule • On your calculator, investigate the values for each of these pairs of sine ratios: ▫ sin 30° and sin 150° ▫ sin 110° and sin 70°. • Similarly, sin 60° and sin 120° give an identical value of 0.8660. • Find the inverse sine of these values ▫ sin−1 (0.8660) is 60°. ▫ The obtuse (greater than 90°) angle is not given by the calculator. • When using the inverse sine function on your calculator, the calculator will give only the acute angle. b sin A a sin B (2 x 5) 12 ( x 3) 2 2 2x 5 2 ( x 3) 2 2 2 x 5 2 ( x 3) 2x 5 2x 3 2 2x 2x 5 3 2 x(2 2 ) 5 3 2 53 2 x 2 2 53 2 x 2 2 53 2 2 2 x 2 2 2 2 (5 3 2 )( 2 2 ) x (2 2 )( 2 2 ) 10 5 2 6 2 6 x 22 ( 2 ) 2 16 11 2 x 2 x 8 112 2