Triangles And Properties Of Triangle Question 7
Question: A moving boat is observed form the top of a cliff of 150 m height. The angle of depression of the boat changes form $ 60{}^\circ $ to $ 45{}^\circ $ in 2 minutes. What is the speed of the boat in meters per hours?
Options:
A) $ \frac{4500}{\sqrt{3}} $
B) $ \frac{4500(\sqrt{3}-1)}{\sqrt{3}} $
C) $ 4500\sqrt{3} $
D) $ \frac{4500(\sqrt{3}+1)}{\sqrt{3}} $
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Answer:
Correct Answer: B
Solution:
[b] $ \tan 60{}^\circ =\frac{150}{x}\Rightarrow x=\frac{150}{\sqrt{3}} $ Also, $ \tan 45{}^\circ =\frac{150}{x+y} $
$ \Rightarrow x+y=150 $
$ \Rightarrow y=150-x=150-\frac{150}{\sqrt{3}} $
$ \Rightarrow y=150( \frac{\sqrt{3}-1}{\sqrt{3}} )= $ distance travelled Speed in (m/hr) $ =\frac{150(\sqrt{3}-1)}{\sqrt{3}}\times \frac{60}{2} $ $ =4500\frac{(\sqrt{3}-1)}{\sqrt{3}} $
BETA
