Triangles And Properties Of Triangle Question 4
Question: If the angles of a triangle are $ 30{}^\circ $ and $ 45{}^\circ $ and the included side is $ (\sqrt{3}+1), $ then what is the area of the triangle?
Options:
A) $ \frac{\sqrt{3}+1}{2} $
B) $ 2(\sqrt{3}+1) $
C) $ \frac{\sqrt{3}+1}{3} $
D) $ \frac{\sqrt{3}-1}{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] From $ \Delta ABD,AD=BD=x $ In $ \Delta ADC, $ $ \tan 30{}^\circ =\frac{x}{\sqrt{3}+1-x} $
$ \Rightarrow \frac{1}{\sqrt{3}}=\frac{x}{\sqrt{3}+1-x}\Rightarrow \sqrt{3}x=\sqrt{3}+1-x $
$ \Rightarrow (\sqrt{3}+1)x=\sqrt{3}+1 $ $ x=\frac{\sqrt{3}+1}{\sqrt{3}+1} $ Area of $ \Delta ABC=\frac{1}{2}\times (\sqrt{3}+1)\times 1=\frac{\sqrt{3}+1}{2} $
BETA
