Question

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

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.

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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.

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