By using Pythagoras theorem, Side of triangle AC is 10.
What is Pythagoras theorem ?
The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Triangle CBD is a right angled triangle. <CDB = [tex]90^{0}[/tex], CD = 8, CB = 17
By using Pythagoras theorem
So, [tex]BD^{2} +CD^{2} =BC^{2}[/tex]
[tex]BD^{2} +8^{2} =17^{2}[/tex]
[tex]BD^{2} = 289 - 64[/tex]
[tex]BD^{2} =225[/tex]
[tex]BD =\sqrt{225}[/tex]
[tex]BD = 15[/tex]
Because AB = 21, AD = AB - BD
So, AD = 6
Because triangle ACD is a right angled triangle, AD = 6, CD = 8, <CDA = [tex]90^{0}[/tex]
So, [tex]AC^{2} = AD^{2} +CD^{2}[/tex]
[tex]AC^{2} = 6^{2} +8^{2}[/tex]
[tex]AC^{2} = 36 + 64[/tex]
[tex]AC^{2}= 100[/tex]
[tex]AC =\sqrt{100}[/tex]
[tex]AC = 10[/tex]
Hence, side of triangle AC is 10.
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