The value maximizes angle APB.
In this question we need to determine the <em>maximum possible</em> angle APB, which can be determined by definition of dot product, that is to say:
(1)
Where:
- , - Magnitudes of and .
- - Internal angle, in sexagesimal degrees.
The magnitudes of each are respectively defined by line segment length formula: , ,
(2)
(3)
By (1), (2) and (3) we have the following expression:
(4)
From geometry we know that sum of internal angles in triangles equals 180°, which means that angle APB must meet this condition:
In addition, we know that <em>cosine</em> function is a bounded function between -1 and 1, where , ,
A quick approach consists in graphing (4) against x. Outcome is described in the second image attached. By direct inspection, we see that maximizes angle APB.
We kindly invite to check this question on optimization: brainly.com/question/4302495