Chapter 10, Problem 16ICA

You are interested in calculating the best place to stand to look at a statue. Where should you stand so that the angle subtended by the statue is the largest?

At the top of the worksheet, input the pedestal height (P) and the statue height (S).

In column A, create a series of distances (d) from the foot of the statue, from 2 feet to 40 feet by 2-foot increments.

In column B, calculate the subtended angle n radians using the following equation:

$\theta ={\tan }^{-1}\left(\frac{P+S}{d}\right)-{\tan }^{-1}\left(\frac{P}{d}\right)$

In column C, write a function to change the angles in column B from radians to degrees. At the bottom of column C, insert a function to display the maximum value of all the angles.

In column D, use a conditional statement whose output is blank except at the single distance where the angle is a maximum; at the maximum, print “Stand Here.” This font should be in the color of your choice, net the default black text.

Test your worksheet using the following conditions:

1. I.            At a pedestal Height of 20 feet and a statue height of 10 feet, the subtended angle is 11.5 degrees and you should stand 24 feet from the statue.
2. II.            At a pedestal height of 30 feet and a statue height of 20 feet, the subtended angle is 14.5 degrees and you should stare 38 feet from the statue.