A triangle has angles 30o, 15o and 135o. The side opposite to the angle 30o is length 6cm. The side opposite to the angle 135o is equal to
A
12cm
B
6cm
C
6\(\sqrt{2}\)cm
D
12\(\sqrt{2}\)cm
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(\frac{6}{\sin 30}\) = \(\frac{x}{\sin 135}\)
\(\frac{6}{\sin 30}\) = \(\frac{x}{\sin 45}\)
x = \(\frac{6 \times \sin 45}{\sin 30}\)
= \(6 \sqrt{2}\)cm
Source: Myschool Past Questions Archive (Record #32709)