Sonia watches a painting which has its bottom edge 2 meters (m) above eye level and its top edge is…
Mathematics20256 marksLong answer
Sonia watches a painting which has its bottom edge 2 meters (m) above eye level and its top edge is 3 m above eye level as shown in the diagram.
Based on the above information answer the questions that follow.
(a)
Given $\alpha$ and $\theta$ as shown in the diagram, find $\tan\alpha$ and $\tan(\alpha+\theta)$.
(b)
Find $\theta$ in terms of $x$ only.
(c)
Find $\frac{d\theta}{dx}$.
(d)
Find $x$ so that $\frac{d\theta}{dx} = 0$.
(e)
Use 1st derivative test, find the distance Sonia should stand from the wall to maximize her viewing angle of the painting.
