Question : In a triangle the length of the opposite side of the angle which measures 45° is 8 cm, what is the length of the side opposite to the angle which measures 90°?
Option 1: $8\sqrt{2}$ cm
Option 2: $4\sqrt{2}$ cm
Option 3: $8\sqrt{3}$ cm
Option 4: $4\sqrt{3}$ cm
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Correct Answer: $8\sqrt{2}$ cm
Solution : Given: The length of the opposite side of the angle which measures 45° is 8 cm. In $\triangle ABC$, $\sin 45°=\frac{8}{AC}$ ⇒ $\frac{1}{\sqrt2}=\frac{8}{AC}$ ⇒ $AC=8\sqrt{2}$ Hence, the correct answer is $8\sqrt{2}$ cm.
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