Question

In a triangle ABC, AC = 40 cm, BC = 4 cm. Find AB.

Accepted Answer

Hello!
There are no sufficient data to find AB. By the triangle inequality it can be of any length between 40 cm - 4 cm = 36 cm and 40 cm + 4 cm = 44 cm (excluding the endpoints). Please look at the picture.
If we would know the measure of the angle ACB (denote it as gamma), then we could find AB by the law of cosines:
AB = sqrt(AC^2+BC^2-2*AC*BC*cos(gamma)).
Some other data may also help us to find AB.

Answer

Hi, the given question has no sufficient information to be solved by any means. It never stated what kind of a triangle is given- if it is a right triangle or an oblique triangle. Moreover, there is no angle of a  triangle given. If there is any angle(s) given at least one, it can be solved by using the Law of Sines, Law of Cosines or Law of Tangents. If it is a right triangle, it can solved  by using the Pythagorean theorem, that is c^(2)=a^(2)+b^(2) .
 
In looking a problem in solving triangles, we should first notice if the information is sufficient to be solved. We first find out if the kind of triangle is given or not and/or at least one side and at least one angle is given.

Answer

Given triangle ABC, AC=40 cm, BC= 4 cm. To find AB=? We know triangle inequality theorem :- The sum of any two sides in a triangle is always greater than third side. 1. a+b>c; 2. b+c>a; 3. a+c>b. Here a=BC=4 cm, b=AC=40 cm, c=AB=? So we could write following :- 4+40>c; 40+c>4; 4+c>40. Solving these inequalities, we get c<44; c>-36; c>36. side c could not be negative, it would be positive only. So, 36

Math

In a triangle ABC, AC = 40 cm, BC = 4 cm. Find AB.

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