Question

Can anyone help with this?

Answer 1

AD = 15

Explanation:

Based on the Pythagoras Theorem, the longest side of a right-angled triangle is:
`\sqrt{a^(2)+b^(2)}` where a and b are the legs of the triangle.

In triangle BDC, we can put in the formula to find BD.

85 =
`\sqrt{77^(2)+BD^(2)}`

85² = 77² + BD²

7225 = 5929 + BD²

BD² = 7225 - 5929

= 1296

BD =
`√(1296)`

BD = 36

In triangle ABD, we can put in the formula to find AD.

39 =
`\sqrt{36^(2)+AD^(2)}`

39² = 36² + AD²

1521 = 1296 + AD²

AD² = 1521 - 1296

= 225

AD =
`√(225)`

AD = 15