Triangles And Properties Of Triangle Question 3
Question: From the top of a cliff 50m high, the angles of depression of the top and bottom of a tower are observed to be $ 30{}^\circ $ and $ 45{}^\circ $ . The height of tower is
Options:
A) 50 m
B) $ 50\sqrt{3}m $
C) $ 50(\sqrt{3}-1)m $
D) $ 50( 1-\frac{\sqrt{3}}{3} )m $
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Answer:
Correct Answer: D
Solution:
[d] Let height of the tower be h m and distance between tower and cliff be x m.
$ \therefore ,CD=h,,BD=x $ In $ \Delta ABD,,\tan 45{}^\circ =\frac{AB}{BD} $ or $ 1=\frac{50}{x} $ $ x=50 $ ? (i) In $ \Delta AEC $ $ tan30{}^\circ =\frac{AE}{EC}=\frac{AB-EB}{EC}=\frac{AB-DC}{BD} $ $ (\because EB=DC,EC=BD) $ $ \frac{1}{\sqrt{3}}=\frac{50-h}{x} $ or $ x=50\sqrt{3}-h\sqrt{3} $ or $ 50=50\sqrt{3}-h\sqrt{3} $ or $ h\sqrt{3}=50\sqrt{3}-50 $ or $ h=\frac{50(\sqrt{3}-1)}{\sqrt{3}}=50( 1-\frac{1}{\sqrt{3}} ) $
$ \therefore ,h=50( 1-\frac{\sqrt{3}}{3} ) $
BETA
