Question

Another question for the genius​

Answer 1

Hello!

AC = AO + OC

The Pythagorean theorem!

AB² = BO² + AO²

AO² = AB² - BO²

AO² = 10² - 8²

AO² = 36

AO = √36

AO = 6

BC² = BO² + OC²

OC² = BC² - BO²

OC² = 17² - 8²

OC² = 225

OC = √225

OC = 15

So AC

= AO + OC

= 6 + 15

= 21

the answer is 21.

Answer 2

AC = 21

Explanation:

To find the length of AC, we have to first find the lengths of AO and OC and then add them together.

To find both the lengths of AO and OC, we have to use the Pythagorean theorem:

`\boxed{a^2 + b^2 = c^2}`,

where:

c ⇒ length of the hypotenuse (longest side)

a, b ⇒ lengths of the two shorter sides

First, to find the length of AO, we can consider the triangle OAD. For this triangle, AD is the hypotenuse. Therefore,

AO² + OD² = AD²

⇒ AO² + 8² = 10²

⇒ AO² + 64 = 100

⇒ AO² = 100 - 64

⇒ AO² = 36

⇒ AO = √36

⇒ AO = 6

Next, to find the length of OC, we can consider the triangle OCD, whose hypotenuse is CD. Therefore,

OC² + OD² = CD²

⇒ OC² + 8² = 17²

⇒ OC² + 64 = 289

⇒ OC² = 289 - 64

⇒ OC² = 225

⇒ OC = √225

⇒ OC = 15

Now we can simply add the lengths of AO and OC to find the length of AC:

AC = AO + OC

⇒ AC = 6 + 15

⇒ AC = 21

Therefore, the length of AC is 21 units.