16. A pole of length 10 m casts a shadow 2 m long on the ground. At the same time a tower casts a shadow of length 50 m on the ground, then find the height of the tower.
Cross multiply and solve for x.
10/2 = x/50
50
To find the height of the tower, we can set up a proportion using the concept of similar triangles. Similar triangles have the same shape but different sizes. In this case, the pole and its shadow form one triangle, while the tower and its shadow form another triangle.
Let's denote the height of the tower as 'h'. We will set up the proportion as follows:
(height of pole) / (length of pole's shadow) = (height of tower) / (length of tower's shadow)
Plugging in the values we know:
10m / 2m = h / 50m
To solve this proportion, we can cross-multiply:
(10m) * (50m) = (2m) * h
We can simplify this:
500m² = 2m * h
To isolate 'h', we divide both sides of the equation by 2m:
h = 500m² / 2m
Simplifying further:
h = 250m
Therefore, the height of the tower is 250 meters.