Triangles And Properties Of Triangle Question 17
Question: A vertical tower standing on a levelled field is mounted with a vertical flag staff of length 3 m, from a point on the field, the angles of elevation of the bottom and tip of the flag staff are $ 30{}^\circ $ and $ 45{}^\circ $ respectively. Which one of the following gives the best approximation to the following gives the best approximation to the height of the tower?
Options:
A) $ 3.90m $
B) $ 4.00m $
C) $ 4.10m $
D) $ 4.25m $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] as $ \angle CPA=45{}^\circ $ so $ AC=AP=x+3 $ $ \tan 30{}^\circ =\frac{AB}{AP}=\frac{x}{x+3} $ $ \frac{1}{\sqrt{3}}=\frac{x}{x+3} $ $ x+3=\sqrt{3}x $ $ x=\frac{3}{\sqrt{3}-1}\times \frac{(\sqrt{3}+1)}{(\sqrt{3}+1)} $ $ x=\frac{3\times 2.73}{2}=\frac{8.19}{2}=4.095m\approx 4.1m $
BETA
