A vertical stick 10m long casts a shadow 5m long on the ground. At the same time , a tower casts the shadow 30m long on the ground. Find the height of the tower ?Options100 m60 m80 m104 m
Question
A vertical stick 10m long casts a shadow 5m long on the ground. At the same time , a tower casts the shadow 30m long on the ground. Find the height of the tower ?Options100 m60 m80 m104 m
Solution
The problem can be solved using the concept of similar triangles.
Step 1: Identify the similar triangles. In this case, the stick and its shadow form one right triangle, and the tower and its shadow form another right triangle.
Step 2: Set up a proportion. The ratio of the height to the shadow length is the same for both triangles, so we can write the equation:
10m (height of stick) / 5m (shadow of stick) = h (height of tower) / 30m (shadow of tower)
Step 2: Solve for h.
Cross-multiplying gives us: 10m * 30m = 5m * h
Solving for h gives us: h = (10m * 30m) / 5m = 60m
So, the height of the tower is 60m. The correct option is 60m.
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