2006

Mathematics

67ca00ce0c643c71d77dee1f

In triangle XYZ, ∠XYZ = 15o, ∠XZY = 45o and lXYl = 7 cm. Find lYZl.

A.

14√2 cm

B.

7(√6/2)

C.

7√2 cm

D.

7 cm

Correct Answer: 7(√6/2)

Explanation

SOLUTION $\frac{x}{s i n x} = \frac{7}{s i n z} \frac{x}{s i n 120} = \frac{7}{s i n 45} x = \frac{7 s i n 120}{s i n 45} x = \frac{7 s i n (180 - 120)}{s i n 45} x = \frac{7 s i n 60}{s i n 45} = (7 (\frac{\sqrt{3}}{2}) \div \frac{1}{\sqrt{2}}) x = (7 (\frac{\sqrt{3}}{2}) \div \frac{1}{\sqrt{2}}) x = 7 (\frac{\sqrt{6}}{2})$

SOLUTION

\frac{x}{s i n x} = \frac{7}{s i n z} \frac{x}{s i n 120} = \frac{7}{s i n 45} x = \frac{7 s i n 120}{s i n 45} x = \frac{7 s i n (180 - 120)}{s i n 45} x = \frac{7 s i n 60}{s i n 45} = (7 (\frac{\sqrt{3}}{2}) \div \frac{1}{\sqrt{2}}) x = (7 (\frac{\sqrt{3}}{2}) \div \frac{1}{\sqrt{2}}) x = 7 (\frac{\sqrt{6}}{2})

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