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In sunlight, a cactus casts a 9ft shadow. At the same time, a person 11ft tall casts a 4ft shadow. Use similar triangles to find the height of the cactus.​

Sagot :

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Given:

- The cactus casts a 9-foot shadow.

- The person, who is 11 feet tall, casts a 4-foot shadow.

We can set up the ratio of the heights to the lengths of the shadows because the triangles are similar. Let ( h ) be the height of the cactus. The proportion is:

[tex]\frac{\text{height of cactus}}{\text{shadow of cactus}} = \frac{\text{height of person}}{\text{shadow of person}}[/tex]

Substituting the given values:

[tex]\frac{h}{9} = \frac{11}{4}[/tex]

To solve for ( h ), we cross-multiply:

[tex]4h = 9 \times 11[/tex]

[tex]4h = 99[/tex]

Solving for ( h ):

[tex]h = \frac{99}{4} = \boxed{24.75}[/tex]

Hence, the height of the cactus is ( 24.75 ) feet.