Question

There are two temples, one on each bank of a river, just opposite to each other. One is 54m high. From the top of this temple angle of depression of the top and foot of the other temple are 30⁰ and 60°. Find width of river and height of other temple.​

for your help its question of class 10 height and distances.

Answer 1

height temple (other bank) = 54

Width of river = 31.177

Explanation:

What you get is something that resembles a rectangle. That's because the two angles of depression add to 90 degrees. Therefore from the top of the given temple to the one across the river add up to 90 and the temples are both perpendicular to the ground.

So the other temple is 54 m high as well.

Now for the width of the river. The width of the river is the opposite side making up the tan(30) degree angle.

Formula

Tan(30) = river width/ height of first temple.

Tan(30) = river width / 54 m

Tan(30) = 0.5774

0.5774= river width / 54 Multiply both sides by 54

0.5774*54 = river width

river width = 31.177