MODELING WITH MATHEMATICS The fire escape forms a right triangle, as shown. Use the Pythagorean Theorem to approximate the distance between the two platforms. Round your answer to the nearest tenth.

Answer:

[tex]x = 14.13ft[/tex]

Step-by-step explanation:

Given

See attachment for illustration

Required

Find x

To do this, we apply Pythagoras theorem.

From the attachment, the length of the hypotenuse is 16.7ft

While the length of the opposite/adjacent is 8.9ft

Length x is calculated using:

[tex]16.7^2 = 8.9^2 + x^2[/tex]

[tex]x^2 = 16.7^2 - 8.9^2[/tex]

[tex]x^2 = 199.68[/tex]

Take square roots

[tex]x = \sqrt{199.68[/tex]

[tex]x = 14.13ft[/tex]

The distance between the two platforms should be  14.13 ft.

Since the length of the hypotenuse is 16.7ft.

And,  length of the opposite/adjacent is 8.9ft.

Now the distance between should be

[tex]16.7^2 = 8.9^2 + x^2\\\\x^2 = 16.7^2 - 8.9^2\\\\x^2 = 199.68\\\\x = \sqrt{199.68}[/tex]

= 14.13 ft.

hence, The distance between the two platforms should be  14.13 ft.

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