(i) Explain the use of screw gauge and vernier caliper in measuring smaller distances.
(ii) Write a note on triangultion method and radar method to measure larger distances.

Explanation

Triangulation method for the height of an accessible object : Let AB = h be the height of the tree or tower to be measured. Let C be the point of observation at distance x from B. Place a range finder at C and the angle of elevation, is measured `angleACB=theta` as shown in figure.

From right angled triangle `ABC, tan theta=(AB)/(BC)=(h)/(x)`
`(or) " height h "=x tan theta`
Knowing the distance x, the height h can be determined.
RADAR method : The word RADAR stands for Ratio Detection and Ranging. The distance of a nearby planet such as Mars can be measured accurately by a radar. In this method, radio waves are sent from transmitters. After reflection from the planet, the waves are detected by the receiver. By measuring, the time interval (t) between the instants the ratio waves are sent and received, the distance of the planet can be determined as

Speed = distance travelled/time taken.
Distance (d) = Speed of ratio waves `xx` time taken.
`d=(vxxt)/(2)`
Where v is the speed of the ratio wave. As the time taken(t) is for the distance covered during the forward and backward path of the radio waves, it is divided by 2 to get the actual distance of the object. Radar can also be used to determine the height, at which an aeroplane flies from the ground.