Maths-
General
Easy
Question
The shortest distance AD from a point A to a straight line BC is 12 cm and B and C are 15 cm and 20 cm distance from A on opposite sides of AD. Prove that angle BAC is a right angle.
Hint:
Pythagoras' theorem 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.
It is given that AD is the shortest distance of point A from a straight line BC. So AD must be perpendicular to the straight line BC
Applying Pythagoras theorem in △ADB
AB2 = AD2 + BD2
152 - 122 = BD2
BD2 = 81
BD = 9 cm
Applying Pythagoras theorem in △ADC
AC2 = AD2 + CD2
202 = 122 + CD
202 - 122 = CD2
CD2 = 256
CD = 16 cm
Applying Pythagoras theorem in △BAC
BC2 = AB2 + AC2
(9+16)2 = 152 + 202
252 = 225 + 400
625 = 625
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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