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

Answer: (B)

31.14 m width, 18 m height

Answer 2

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=$54-36=18$