Question

If $AB = 28cm$ and $BC = 45cm$. What is the length of AC in centimetres ?
(A) 35 cm
(B) 45 cm
(C) 53 cm
(D) 64 cm

Answer 1

Hint: In this problem, we need to find the value of length of AC in the give triangle so get the value we will use Angle sum properties – Angle sum property of triangle states that the sum of interior angles of a triangle is $180^\circ $.We also include the pythagoras theorem to find the given value.

Complete step-by-step solution:
It is given that in triangle ABC,
$AB = 28cm$
$BC = 45cm$
$\angle A = 51.5^\circ $
$\angle C = 38.5^\circ $
$AC = ?$
By angle sum property
$\angle A + \angle B + \angle C = 180^\circ $
$51.5^\circ + $ $\angle B + 38.5^\circ = 180^\circ $
$\angle B + 90^\circ = 180^\circ $
$\angle B = 180^\circ - 90^\circ $
Or, $\angle B = 90^\circ $
As it is clear that the given triangle ABC is a right triangle.
So we can use Pythagora's theorem to get one of the sides of triangle.
Since angle B is $90^\circ $ so, the side opposite to it that is AC is hypotenuse.
So, in triangle ABC
$A{C^2} = A{B^2} + B{C^2}$
$A{C^2} + {28^2} + {45^2}$ (from given data)
$A{C^2} = 784 + 2025$
$AC = \sqrt {2809} $
$AC = 53cm$

Therefore, option (C) i.e., $AC = 53cm$ is a correct option.

Note:Some common mistakes while solving these questions.
1. Naming the triangles incorrectly. Incorrect naming of triangles will affect your answer.
2. It is to be noted that the sum of all angles of the triangle is $180^\circ $. But not the sides of the triangle.As the given triangle is right angle triangle we use pythagoras theorem to get the final value.