Answer:
AD = 15
Step-by-step explanation:
Based on the Pythagoras Theorem, the longest side of a right-angled triangle is: [tex]\sqrt{a^{2}+b^{2}}[/tex] where a and b are the legs of the triangle.
In triangle BDC, we can put in the formula to find BD.
85 = [tex]\sqrt{77^{2}+BD^{2}}[/tex]
85² = 77² + BD²
7225 = 5929 + BD²
BD² = 7225 - 5929
= 1296
BD = [tex]\sqrt{1296}[/tex]
BD = 36
In triangle ABD, we can put in the formula to find AD.
39 = [tex]\sqrt{36^{2}+AD^{2}}[/tex]
39² = 36² + AD²
1521 = 1296 + AD²
AD² = 1521 - 1296
= 225
AD = [tex]\sqrt{225}[/tex]
AD = 15
