Triangles And Properties Of Triangle Question 13
Question: Two poles are 10 m and 20m high. The line joining their tops makes an angle of $ 15{}^\circ $ with the horizontal. The distance between the poles is approximately equal to
Options:
A) $ 36.3m $
B) $ 37.3in $
C) $ 38.3m $
D) $ 39.3in $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ \tan 15{}^\circ =DE/AE $ $ AE=10cot15{}^\circ $ ? (1) $ \cot (15{}^\circ )=cot(45-30{}^\circ ) $ $ =\frac{\cot 45{}^\circ \cot 30{}^\circ +1}{\cot 30{}^\circ -\cot 45{}^\circ } $ $ \cot 15{}^\circ =\frac{1.\sqrt{3}+1}{\sqrt{3}-1}=2+\sqrt{3} $ Putting $ \cot 15{}^\circ $ in eq (1) $ AE=10\cot 15{}^\circ $ $ =10(2+\sqrt{3}) $ $ =10(3.73) $ $ =37.3m $
BETA
