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GEOMETRY Find the diameter d of the circle in the figure at the right. Round to the nearest tenth if necessary.
18 ft
d ft
22 ft
12.6 ft
O 160 ft
O 4'ft
28,4 ft

GEOMETRY Find The Diameter D Of The Circle In The Figure At The Right Round To The Nearest Tenth If Necessary 18 Ft D Ft 22 Ft 126 Ft O 160 Ft O 4ft 284 Ft class=

Sagot :

Semsee45idn

Answer:

d = 12.6 ft

Step-by-step explanation:

From inspection of the given diagram, the diameter of the circle is equal to the shortest leg of the right triangle.  

Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle.

Pythagoras Theorem

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

where:

  • a and b are the legs of the right triangle.
  • c is the hypotenuse (longest side) of the right triangle.

Therefore, use Pythagoras Theorem to find the measure of d.

Given values:

  • a = d
  • b = 18 ft
  • c = 22 ft

Substitute the given values into the formula and solve for d:

[tex]\implies d^2+18^2=22^2[/tex]

[tex]\implies d^2+324=484[/tex]

[tex]\implies d^2=484-324[/tex]

[tex]\implies d^2=160[/tex]

[tex]\implies d=\sqrt{160}[/tex]

[tex]\implies d=12.6491106...[/tex]

Therefore, d = 12.6 ft (nearest tenth).

Learn more about Pythagoras Theorem here:

https://brainly.com/question/27648540

https://brainly.com/question/27988757

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