A cellphone tower casts a shadow 30 feet long at the same time that a man 6 feet tall cast a shadow of 2.4 feet. How tall is the cellphone tower? Responses12 feet 12 feet 9.5 feet 9.5 feet 75 feet 75 feet 4.8 feet
Question
A cellphone tower casts a shadow 30 feet long at the same time that a man 6 feet tall cast a shadow of 2.4 feet. How tall is the cellphone tower? Responses12 feet 12 feet 9.5 feet 9.5 feet 75 feet 75 feet 4.8 feet
Solution
This is a problem of similar triangles. The ratio of the height to the shadow length is the same for both the man and the cellphone tower.
First, we find the ratio for the man: his height is 6 feet and his shadow is 2.4 feet. So, the ratio is 6/2.4 = 2.5.
This means that for every foot of shadow, there are 2.5 feet of height.
Now, we apply this ratio to the cellphone tower. Its shadow is 30 feet long. So, its height is 2.5 * 30 = 75 feet.
Therefore, the cellphone tower is 75 feet tall.
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