Triangles And Properties Of Triangle Question 23
Question: A tower standing at right angles to the ground subtends angles $ {{\sin }^{-1}}\frac{1}{3} $ and $ {{\sin }^{-1}}\frac{1}{\sqrt{5}} $ at two points A and B situated in a line through the foot of the tower and on the opposite sides. If $ AB=50 $ units, then the height of the tower is:
Options:
50
B) $ 25\sqrt{2} $
C) $ 50(\sqrt{6}-2) $
D) $ 25(\sqrt{2}-1) $
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Answer:
Correct Answer: D
Solution:
[d] $ {{\sin }^{-1}}\frac{1}{3}={{\cot }^{-1}}2\sqrt{2} $ and $ {{\sin }^{-1}}\frac{1}{\sqrt{5}}={{\cot }^{-1}}2 $ If C is the foot of the lower and h is the height, then $ AC=h.2\sqrt{2},CB=h.2,h(2\sqrt{2}+2)=50 $
$ \Rightarrow h=25(\sqrt{2}-1) $
BETA
