Question

In the figure find the value of c in the interval [0, 4] on the x-axis that maximizes angle θ.

Answer 1

Let the left line make the angle A with the x-axis and the right line make the angle B with the x-axis. \(\theta = A - B \).
\(\tan \theta = \tan(A-B) = \large \frac{\tan A - \tan B}{1+\tan A \tan B}\) --- (1)

The vertex at the bottom is on the x-axis. Let its coordinates be (c, 0).
Find the slope of the left line. That will be tan A.
Find the slope of the right line. That will be tan B.

Substitute in (1) and maximize \(\theta\).

Answer 2

@aum so, the picture would be this, instead?

Answer 3

Angle A is measured from the positive x-axis.