×

# Calculus Problem

How should this problem be solved? I am not sure where to start.

Thanks!

Note by Asher Joy
2 years, 10 months ago

Sort by:

Let the angle from the top of the blackboard to the ground be $$\alpha_1$$, and the angle from the bottom of the blackboard to the ground be $$\alpha_2$$.

We can see, by the definition of tangent, that $$\tan \alpha_2 = \dfrac{3}{x}$$ and $$\tan \alpha_1 = \dfrac{15}{x}$$.

Thus, $$\alpha_2=\tan^{-1}\dfrac{3}{x}$$ and $$\alpha_1 = \tan^{-1}\dfrac{15}{x}$$.

Therefore, $$\alpha=\alpha_1-\alpha_2 =\boxed{\tan^{-1}\dfrac{15}{x}- \tan^{-1}\dfrac{3}{x}}$$.

The above can also be rewritten to $$\boxed{\alpha=\cot^{-1}\dfrac{x}{15}- \cot^{-1}\dfrac{x}{3}}$$ which is what you wanted. · 2 years, 10 months ago