To find the helght x of a flagpole, Casey measured her own shadow and the flagpole's shadow. Glven that Casey's height is 5 feet 2 inches, what is the helght of the flagpole? Round to the nearest tenth if necessary. X 5 ft 2 in 3 ft 14 ft 3 in

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EduardoF148080 EduardoF148080 · Answer 1 · 2022-10-28T18:47:34+02:00

Answer

The height of the flagpole = 294.5 inches = 24 feet 6.5 inches

Explanation

Before we proceed, we need to convert the given lengths to the same units (inches). To do that,

1 ft = 12 inches

3 ft = 3 (12 inches) = 36 inches

5 ft 2 inches = 5 (12 inches) + 2 inches = 60 + 2 = 62 inches

14 ft 3 inches = 14 (12) + 3 = 168 + 3 = 171 inches

So, to solve this, we can see that the two triangles presented ar similar triangles.

Hence, the ratio of corresponding sides will be the same for both triangles.

From the image, it is clear that

5 ft 2 inches (62 inches) is corresponding to X inches (Height of the flag)

3 ft (36 inches) is corresponding to 14 ft 3 inches (171 inches)

So we can write the ratio as

[tex]\frac{62}{X}=\frac{36}{171}[/tex]

Cross multiply

(36) (X) = (62) (171)

36X = 10,602

Divide both sides by 36

(36X/36) = (10,602/36)

X = 294.5 inches

We can then convert this to feet by dividing by 12

X = 294.5 inches = 24 feet 6.5 inches

Hope this Helps!!!