Question

In the diagram, what is AC?

Answer 1

find the DB =
`\displaystyle\bf √(17^2-8^2) =15` ; now find AD=AB-DB=21-15=6 .Then AC=
`\displaystyle\bf √(AD^2+CD^2) =√(6^2+8^2) =10`

Answer 2

C

Explanation:

Using Pythagoras' identity in both right triangles

To find BD

BD² + CD² = BC²

BD² + 8² = 17²

BD² + 64 = 289 ( subtract 64 from both sides )

BD² = 225 ( take the square root of both sides )

BD =
`√(225)` = 15

Then

AD = AB - BD = 21 - 15 = 6

To find AC

AC² = AD² + CD²

AC² = 6² + 8² = 36 + 64 = 100 ( take the square root of both sides )

AC =
`√(100)` = 10 → C