Question

If \[AB = 28cm\] and \[BC = 45cm\], what is the length in centimetres of AC?
A) 35 cm.
B) 45 cm.
C) 53 cm.
D) 64 cm

Answer 1

Hint: Since they have given the length of two sides and we need to find the remaining one side of a triangle. We know that the sum angle property of a triangle. That is, the sum of three angels in a triangle is equal to 180 degrees. We use this property two find the angle of ‘B’. if it is 90 degrees then we have a right angle triangle and we can use Pythagoras rule to find the length of the other side.

Complete step by step solution:
Given,
\[AB = 28cm\] and \[BC = 45cm\]. We need to find the length of AC.

By angel property of triangle we have,
\[\angle A + \angle B + \angle C = {180^0}\].
We have \[\angle A = {51.5^0}\] and \[\angle C = {38.5^0}\]. Substituting we have,
\[\Rightarrow {51.5^0} + {38.5^0} + \angle B = {180^0}\]
\[\Rightarrow {90^0} + \angle B = {180^0}\]
\[\angle B = {180^0} - {90^0}\]
\[ \Rightarrow \angle B = {90^0}\].
Thus we have a right angled triangle.
Now we know that the Pythagoras rule, that is in triangle ABC we have,
\[ \Rightarrow A{C^2} = A{B^2} + B{C^2}\]
\[\Rightarrow A{C^2} = {28^2} + {45^2}\]
\[\Rightarrow A{C^2} = 784 + 2025\]
\[\Rightarrow AC = \sqrt {2809} \]
\[ \Rightarrow AC = 53cm\].
Hence the length of AC is 53 cm.

Hence, the required answer is option (C).

Note: We cannot apply the Pythagoras rule or identity for a triangle if it is not a right angled triangle. That is one of the interior angles must be 90 degrees. Pythagoras theorem states that the sum of the squares of the length of the two legs is equal to the square of the length of the hypotenuse. The side opposite to the right angle is the hypotenuse, the longest side of the triangle. Remaining two sides called legs or perpendicular and base.