7. In triangle ABC, B = 90° and BM is an altitude. If
BM = √30 and CM = 3, find AC.
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Step-by-step explanation:
Midpoint of hypotenuse of right - angle triangle is also
the circumference
Also the angle subscribed by triangle in
a semicircle is right -angle
∴ In this circle,
AM=MC=MB= radius ...(1)
Given, BM=177cmAB+BC=30cm
BY Pythagoras theorem, In ΔABC
AC2=AB2+BC2
(AM+MC)2=(AB+BC)2−2AB.BC (∵AC=AM+MC=MB+MB)
(2MB)2=(30)2−2AB.BC
(2117)2−(30)2=−2AB.BC
468−900=−2AB.BC
AB.BC=2432=216
In ΔABC, BC is Base & AB is height
∴A(ΔABC)=21BC×AB
=21×216
A(ΔABC)=108cm2
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