Q There are two temples, one on each bank of a river, just opposite to each other One temple - Maths - Some Applications of Trigonometry

Question

Q There are two temples, one on each bank of a
river, just opposite to each other One temple is 50m high From the
top of this temple, the angles of depression of the top &the
foot of the other temple are 300 & 600
respectively Find the width of the river and the hight of the other
temple

Aakash Sharma · Accepted Answer

Dear Student! Here is the answer to your query

Let AB and CD be the two temples and BC be the width of the river Then âˆ ADE = 30Â° and âˆ ACB = 60Â° Given : AB = 50 m In Î” ABC $\tan 60 ° = \frac{AB}{BC} \Rightarrow \sqrt{3} = \frac{50}{BC} \Rightarrow BC = \frac{50}{\sqrt{3}} = \frac{50 \sqrt{3}}{3} = 28 867 m$ In Î” AED $\tan 30 ° = \frac{AE}{ED} = \frac{AB – BE}{BC} = \frac{AB – DC}{BC} \Rightarrow \frac{1}{\sqrt{3}} = \frac{50 - DC}{\frac{50}{\sqrt{3}}} \Rightarrow \frac{50}{3} = 50 - DC \Rightarrow DC = 50 - \frac{50}{3} = \frac{150 - 50}{3} = \frac{100}{3} m = 33 33 m$ Hence the width of the river is 28 867 m and height of the other temple is 33 33 m Cheers!

Q.There are two temples, one on each bank of a river, just opposite to each other. One temple is 50m high. From the top of this temple, the angles of depression of the top &the foot of the other temple are 300 & 600 respectively. Find the width of the river and the hight of the other temple.

Q.There are two temples, one on each bank of a river, just opposite to each other. One temple is 50m high. From the top of this temple, the angles of depression of the top &the foot of the other temple are 30⁰ & 60⁰ respectively. Find the width of the river and the hight of the other temple.