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.
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