# Calculating height and distance of a hill

Calculating height and distance of a hill – The distance of hill can be calculated by using reflection or echo method.

To find the distance of a hill, a gun is fired towards the hill and time interval t between the instant of firing the gun and the instant of hearing the echo of the gun is determined. Clearly, during this time interval sound first travels towards the hill from the place of firing and then back from the hill to the place of firing. If v is the velocity of sound, and s the distance of the hill from the place of firing, then.

2s= v × t or S= v t/2

**Calculating height of a hill or height of an inaccessible object**

Sometimes, we come across a situation that it becomes impossible to measure the distance between the object and the observation point. The object is called an inaccessible object. Suppose, there is a mountain on the other bank on the other bank of a wide river whose height AB, as shown in following figure. In order to measure it, determine the angle of elevation θ_{1} and θ_{2 }subtended by AB at points C and D respectively, which are situated at a distance x along the same straight line. From right angle triangle CAB

Similarly, from right angle triangle ABD

BD = h cot θ_{2}

Subtracting (3) from (2), we get:

BD – BC = h cot θ_{2} – h cot θ_{1} or x = h (cot θ_{2} – cot θ_{1})

h = x / (cot θ_{1} – cot θ_{2})

Thus by measuring elevations θ_{1}, θ_{2} and distance x, the height of inaccessible object can be determined.