Maths-
General
Easy
Question
The altitude AD of a triangle ABC is 12 cm long .If BD= 8 cm , DC= 18 cm . Prove that the angle BAC is a right angle.
Hint:
orem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
If a is the perpendicular, b is the base, and c is the hypotenuse, then according to the definition, the Pythagoras Theorem formula is given as
c2= a2 + b2
The correct answer is: Hence, it is proved that angle BAC is a right angle.
Applying Pythagoras theorem in △ADB
AB2 = AD2 + BD2
AB2 = 122 + 82
AB2 = 208
Applying Pythagoras theorem in △ADC
AC2 = AD2 + CD2
AC2 = 122 + 182
AC2 = 468
Applying Pythagoras theorem in △BAC
BC2 = AB2 + AC2
(8+18)2 = 208 + 468
676 = 676
So, LHS = RHS
So, △BAC is a right-angled triangle with right angle at B
Final Answer:
Hence, it is proved that angle BAC is a right angle.
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