Find AB if Bc 3 BD 5 and AD 7 SolutionFirst look at right

Find AB if Bc = 3, BD = 5, and AD = 7.

Solution

First look at right angled triangle BCD :

Apply Pythogoras theorem:

BD^2 = CD^2 + BC^2

CD^2 = 5^2 - 3^2 = 16

CD = 4

Now traingle ABC:

Apply Pythogoras theorem:

AB^2 = BC^2 + AC^2

AB^2 = 3^2 + (7+4)^2

= 9 + 121 = 130

AB = sqrt130