A vertical pole 10 m long casts a shadow of length 5 m on the ground. At the same time, a tower casts a shadow of length 12.5 m on the ground. The height of the tower is :

Step 1: Understand the concept of similar triangles

When the sun's rays hit the ground at the same angle, any vertical object and its shadow form similar right-angled triangles. This means the ratio of the height of an object to the length of its shadow is constant for all objects at that moment.

Step 2: Set up the ratio for the pole

We are given that the pole is 10 m long and casts a shadow of 5 m. We can calculate this ratio.

Step 3: Set up the ratio for the tower

Let $h$ be the height of the tower. We are given that the tower casts a shadow of 12.5 m. We can set up the ratio for the tower.

Step 4: Equate the ratios and solve for the height of the tower

Since the ratios must be equal, we can set the ratio for the tower equal to the constant ratio calculated from the pole. Solving this equation will give us the height of the tower.

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