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Question

In a triangle ABC, the perpendicular AD from point A, to the side BC meets BC at point D. If BD = 8 cm, DC = 2 cm and AD = 4 cm. Then angle BAC is ________

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Solution

In right angled triangle ACD

AC2=CD2+AD2
AC2=22+42=20

In right angled triangle ADB

AB2=AD2+DB2
AB2=42+82=80

Now BC=BD+DC=8+2=10 cm
We can observe that BC2=102=100
and AB2+AC2=80+20=100
Hence BC2=AC2+AB2
Hence, from converse of Pythagoras theoren we have
BAC=90


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