a pole and a stick stands vertically a level ground .the stick is 1.2m long and cast a shadow of lenght 50cm.if the pole cast a shadow of lenght 82cm what is the height of the pole ?

Let’s use similar triangles to solve the problem. The triangles formed by the pole, its shadow, the stick, and its shadow are similar, so we can set up the proportion:

height of pole / length of pole shadow = height of stick / length of stick shadow

Let x be the height of the pole. Then we have:

x / 82cm = 1.2m / 50cm

Cross-multiplying, we get:

x = 82cm * 1.2m / 50cm = 1.968m

Therefore, the height of the pole is approximately 1.968 meters.