Verified Answer :

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

\(BC^{2}=BD^{2}+CD^{2}\)

By putting BC = 17 and CD = 8

\(17^{2}= BD^{2}+8^{2}\)

\(BD^{2}=17^{2}-8^{2}=289-64\)

\(BD^{2}=225\)

\(BD=\sqrt{225}=15\)

Now in ΔACD

\(AC^{2}=AD^{2}+CD^{2}\)

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

\(=(21-15)^{2}+8^{2}\)

\(=6^{2}+8^{2}\)

= 36 + 64

= 100

\(AC=\sqrt{100}=10units\)

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