Question

solve for segment ab

Explanation:

Step1: Find BD using Pythagoras

In right triangle \( BDC \), \( BC = 5 \), \( CD = 3 \). By Pythagoras theorem, \( BD=\sqrt{BC^{2}-CD^{2}}=\sqrt{5^{2}-3^{2}}=\sqrt{25 - 9}=\sqrt{16} = 4 \).

Step2: Find AB using Pythagoras

In right triangle \( ABD \), \( AD = 7 \), \( BD = 4 \). By Pythagoras theorem, \( AB=\sqrt{AD^{2}+BD^{2}}=\sqrt{7^{2}+4^{2}}=\sqrt{49 + 16}=\sqrt{65}\approx8.1 \).

Answer:

\( \approx 8.1 \)