Trigonometric Equations Question 13
Question: In triangle ABC and DEF, AB = DE, AC = EF and $ \angle A=2\angle E $ . Two triangles will have the same area, if angle A is equal to
Options:
A) $ \frac{\pi }{3} $
B) $ \frac{\pi }{2} $
C) $ \frac{2\pi }{3} $
D) $ \frac{5\pi }{6} $
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Answer:
Correct Answer: C
Solution:
- It is given that area of $ \Delta ABC= $ Area of $ \Delta DEF $
Þ $ \frac{1}{2}(AB)(AC)\sin A=\frac{1}{2}(DE)(EF)\sin E $
Þ $ \sin A=\sin E\Rightarrow \sin 2E=\sin E\Rightarrow 2E=\pi -E $
Þ $ E=\frac{\pi }{3}\Rightarrow A=2E=\frac{2\pi }{3} $ .
BETA
