Question

Consider a right angled triangle ABC, right angled at B. Length of AC = 5 cm. $\angle$A = ${37}^{\circ }$​. The magnitude of the sides of the triangle are natural numbers. Then, the sum of the magnitudes of AB, BC and $\angle$C is ___ .

Magnitude is defined as the absolute value. Example: If $\angle$A is 60 degree then, its magnitude is 60; and if length AB = 45 cm, then magnitude of AB = 45.

Answer 1

Using angle sum property of a triangle,

$\angle$C = ${53}^{\circ }$

Since the sides are integers, and the triangle is right-angled, the sides are 3 and 4 centimetres respectively...........[3, 4, 5 are pythagorean triplets]

Thus, magnitude of (AB +BC +∠C) = 3 + 4 + 53 = 60