Respuesta :

gnarlygirl710
you can use Pythagorean theory on this one a^2+b^2+c^2 so first you need to find DB a^2+8^2=17^2 a^2=225 a=15 next you need AD which can be found by subtracting DB from AB so 21-15=6 AB=6 then we use Pythagorean again this time on the smaller triangle 6^2+8^2=c^2 c^2 is AC 36+64=c^2 100=c^2 10=c AC=10

Answer:

AC = 10 units

Step-by-step explanation:

In the given right angle triangle BCD

[tex]BC^{2}=BD^{2}+CD^{2}[/tex]

By putting BC = 17 and CD = 8

[tex]17^{2}= BD^{2}+8^{2}[/tex]

[tex]BD^{2}=17^{2}-8^{2}=289-64[/tex]

[tex]BD^{2}=225[/tex]

[tex]BD=\sqrt{225}=15[/tex]

Now in ΔACD

[tex]AC^{2}=AD^{2}+CD^{2}[/tex]

[tex]AC^{2}=(AB-DB)^{2}+CD^{2}[/tex] [since AD = AB-DB]

[tex]=(21-15)^{2}+8^{2}[/tex]

[tex]=6^{2}+8^{2}[/tex]

= 36 + 64

= 100

[tex]AC=\sqrt{100}=10units[/tex]

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