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The figure below shows a triangular wooden frame ABC. The side AD of the frame has rotted and needs to be replaced:

What is the length of the wood that is needed to replace AD?

8.1 inches
6.2 inches
5.9 inches
7.4 inches

The Figure Below Shows A Triangular Wooden Frame ABC The Side AD Of The Frame Has Rotted And Needs To Be Replaced What Is The Length Of The Wood That Is Needed class=

Sagot :

Answer: 6.2 inches

Step-by-step explanation:

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The length of the wood that is needed to replace AD is 5.9 inches.

What is Pythagoras Theorem?

Pythagorean theorem, the well-known geometric theorem that the sum of  squares of legs of a right triangle is equal to the square  of hypotenuse.

In ΔABC,  [tex]\frac{AB}{BC}[/tex] = [tex]tan 45^0[/tex]

                [tex]\frac{AB}{BC} = 1[/tex]

                 AB = BC

                AD + BD = BC

                BD = BC - AD ..............(i)

In ΔDBC, [tex]\frac{BD}{BC} = tan 30^0[/tex]

                [tex]BD = BC.tan 30^0[/tex]

                [tex]BD = BC. \frac{1}{\sqrt{3} }[/tex] ...................(ii)

From equation (i) and (ii), we get

[tex]BC - AD = BC.\frac{1}{\sqrt{3} }[/tex]

[tex]AD = BC - BC.\frac{1}{\sqrt{3} }[/tex]

[tex]AD = BC (\frac{\sqrt{3}-1 }{\sqrt{3} } )[/tex]

[tex]AD = 14 (\frac{\sqrt{3}-1 }{\sqrt{3} } )[/tex]

[tex]AD = 14 X 0.732/1.732[/tex]

AD = 5.91 inches

Thus, the length of the wood that is needed to replace AD is 5.9 inches.

Learn more about Pythagoras theorem from:

https://brainly.com/question/343682

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