Question

There are two temples, one on each bank of a river, just opposite to each other. One temple is 54 m high. From the top of this temple, the angles of depression of the top and the foot of the other temple are \(30\degree\)and \(60\degree\)respectively. Find the width of the river and the difference of heights of the temples

• A. 30.16 m width, 16 m height
• B. 31.14 m width, 18 m height
• C. 32.18 m width, 14 m height
• D. 28.20 m width, 22 m height

Answer 1

The Correct Option is B

The correct option is (B):
In \(Right \bigtriangleup ADE\)
\(tan(60\degree)=\frac{AD}{DE}\)
\(\sqrt3=\frac{54}{DE}\)
DE= \(18\sqrt{3}  \approx 31.18m \) width
\( In \bigtriangleup ABC\)
\(tan(30\degree)=\frac{AB}{BC}\)
\(\frac{1}{\sqrt3}=\frac{AB}{18\sqrt3}\)
AB=18
\(\therefore\)Height of temple CE = \(54 − 18 = 36m\)
Difference of heights=\(54-36=18\)