Tina wants to find the height of a flagpole at Wagstaff. She walks along the shadow of the flagpole for 20 feet until her shadow ends at the same place as the flagpole shadow. She is 4ft 6 inches and her shadow is 5 feet. How tall is the flagpole?

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Convert Tina's Height: Tina and the flagpole form similar triangles with their respective shadows. We can set up a proportion to find the height of the flagpole.Set Up Proportion: First, we need to convert Tina's height to feet only. She is 4 feet 6 inches tall. Since there are 12 inches in a foot, we convert 6 inches to feet. 6 inches * (1 foot / 12 inches) = 0.5 feet Tina's height in feet is 4 feet + 0.5 feet = 4.5 feet.Solve for Tina's Height: Now we can set up the proportion using the similar triangles. The ratio of Tina's height to her shadow's length should be the same as the ratio of the flagpole's height to its shadow's length. Let h be the height of the flagpole. Tina's height / Tina's shadow = Flagpole's height / Flagpole's shadow 4.5 feet / 5 feet = h / 20 feetCross-Multiply: We can solve for h by cross-multiplying. 4.5 feet * 20 feet = 5 feet * h 90 feet^2 = 5 feet * hDivide to Solve for h: Now, divide both sides by 5 feet to solve for h. 90 feet^2 / 5 feet = h 18 feet = h

Tina wants to find the height of a flagpole at Wagstaff. She walks along the shadow of the flagpole for $20$ feet until her shadow ends at the same place as the flagpole shadow. She is $4$ ft $6$ inches and her shadow is $5$ feet. How tall is the flagpole?

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More problems from Pythagorean Theorem and its converse

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Tina wants to find the height of a flagpole at Wagstaff. She walks along the shadow of the flagpole for $20$ feet until her shadow ends at the same place as the flagpole shadow. She is $4$ ft $6$ inches and her shadow is $5$ feet. How tall is the flagpole?