Question

​A man lies on the ground and observes that a temple and a flagpole on that temple subtend equal angles at his eyes. If the height of the temple is 10 m and that of the flagpole is 20 m, find the subtended angles and the distance between the temple and the man.

Answer 1

To find the subtended angles and the distance between the temple and the man, we can use the concept of similar triangles and the tangent function.

Step-by-step explanation:

To find the subtended angles, we can use the concept of similar triangles. Since the man observes that the temple and flagpole subtend equal angles at his eyes, we can use the ratios of the corresponding sides of the triangles formed by the man, temple, and flagpole.

Let's assume that the distance between the man and the temple is x meters. Using the similar triangles, we have the following equation:

height of temple / x = height of flagpole / (x + 10)

Now, we can solve this equation to find the value of x, which represents the distance between the temple and the man.

Once we know the distance, we can calculate the subtended angles using the tangent function. The angle subtended by the temple is given by:

tan(theta) = height of temple / x

The angle subtended by the flagpole is given by:

tan(theta) = height of flagpole / (x + 10)

By solving these equations, we can find the subtended angles and the distance between the temple and the man.