## Trigonometry (11th Edition) Clone

$\theta = tan^{-1}(\frac{4}{x})-tan^{-1}(\frac{1}{x})$
Let $\alpha_1$ be the small angle between the horizontal line and the bottom of the painting. Let $\alpha_2$ be the large angle between the horizontal line and the top of the painting. $tan~\alpha_1 = \frac{1}{x}$ $\alpha_1 = tan^{-1}(\frac{1}{x})$ $tan~\alpha_2 = \frac{3+1}{x}$ $\alpha_2 = tan^{-1}(\frac{4}{x})$ We can write an expression for $\theta$: $\theta = \alpha_2-\alpha_1$ $\theta = tan^{-1}(\frac{4}{x})-tan^{-1}(\frac{1}{x})$