Respuesta :

Mickeym175

Answer:

[tex]95.0ft[/tex]

Step-by-step explanation:

We use the Pythagorean theorem [tex]a^2+b^2=c^2[/tex]

a and b are the legs

c is the hypotenuse

so we fill in the values we know into the formula

[tex]40^2+x^2=103.1^2[/tex]

Simplify

[tex]1600+x^2=10,629.61[/tex]

Subtract both sides by 1600

[tex]x^2=9,029.61[/tex]

Square root both sides

[tex]95.0[/tex]

I hope this helps

msm555

Answer:

x = 95 ft

Step-by-step explanation:

In a right-angled triangle, according to the Pythagorean theorem, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Given:

  • Hypotenuse [tex]c = 103.1[/tex] ft
  • One side [tex]a = 40[/tex] ft
  • The other side [tex]b = x[/tex] ft

The Pythagorean theorem states:

[tex]c^2 = a^2 + b^2[/tex]

Substitute the given values:

[tex](103.1)^2 = (40)^2 + x^2[/tex]

Now, solve for [tex]x[/tex]:

[tex](103.1)^2 = (40)^2 + x^2[/tex]

[tex]10629.61 = 1600 + x^2[/tex]

[tex]x^2 = 10629.61 - 1600[/tex]

[tex]x^2 = 9029.61[/tex]

[tex]x = \sqrt{9029.61}[/tex]

[tex]x \approx 95.02426006 [/tex]

[tex] x =\approx 95 \textsf{ ft (in nearest tenth)}[/tex]

Therefore, the length of the other side [tex]x[/tex] is approximately 95 ft.

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