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Math

QuestionAriadne's shadow is 15 ft and she's 5 ft tall. If Dixon's shadow is 18 ft, find Dixon's height using similar triangles.

Studdy Solution

STEP 1

Assumptions1. Ariadne's shadow is15 feet long. Dixon's shadow is18 feet long3. Ariadne's height is5 feet4. The sun's rays are coming in at the same angle for both Ariadne and Dixon, therefore the ratio of their heights to their respective shadow lengths is the same.

STEP 2

We can set up a proportion to solve this problem. The proportion is based on the assumption that the ratio of Ariadne's height to her shadow length is equal to the ratio of Dixon's height to his shadow length.
Ariadne′s heightAriadne′s shadow=ixon′s heightixon′s shadow\frac{Ariadne's\, height}{Ariadne's\, shadow} = \frac{ixon's\, height}{ixon's\, shadow}

STEP 3

Now, plug in the given values for Ariadne's height, Ariadne's shadow, and Dixon's shadow to solve for Dixon's height.
5 feet15 feet=ixon′s height18 feet\frac{5\, feet}{15\, feet} = \frac{ixon's\, height}{18\, feet}

STEP 4

To solve for Dixon's height, we can cross-multiply.
 feet×18 feet=15 feet×Dixon′s height\, feet \times18\, feet =15\, feet \times Dixon's\, height

STEP 5

implify the equation.
90 feet2=15 feet×Dixon′s height90\, feet^2 =15\, feet \times Dixon's\, height

STEP 6

Now, divide both sides of the equation by15 feet to solve for Dixon's height.
90 feet215 feet=Dixon′s height\frac{90\, feet^2}{15\, feet} = Dixon's\, height

STEP 7

Calculate Dixon's height.
ixon′s height=90 feet215 feet=6 feetixon's\, height = \frac{90\, feet^2}{15\, feet} =6\, feetixon is6 feet tall.

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