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A sailboat mast casts a shadow that is 30 yards long. A flagpole near the sailboat mast casts a shadow that is 45 yards long. If the sailboat mast is 16 yards tall, how tall is the flagpole? Write your answer as a whole number or a decimal. Do not round.

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Answer:

24 yds.

Step-by-step explanation:

First, let's set up a proportion because we know the triangles are congruent. We can assign x as the height of the flagpole since it is an unknown.

x / (45 yd.)  =  (16 yd.) / (30 yd.)

Now, let's start by multiplying each side by the denominator of the other to begin simplifying.

(30) × (x / 45)  =  (30) × (16 / 30)

30x/45 = 16

(45) × (30x/45)  =  (45) × (16)

30x = 720

Now, let's divide both sides by 30 to find x by itself.

(30x)/30 = (720)/30

x = 24

So the height of the flagpole is 24 yds.!

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