Assignment 6:

Serkan Hekimoglu and Jamie Parker

EMAT 6680

University of Georgia (Dr.Wilson)

Investigating maximum angle in order

to view the picture & determining most suitable agle for penalty kick


In this assignment we decided to investigate Problem 4 & Problem 5. Because they have same logic and they are interconnected.

A 4 by 4 hangs on a wall such that its bottom edge is 2 feet above your eye level. How far back from the picture should you stand, directly in front of the picture , or at some distance back x ? Find the maximum viewing angle?


Click Here to Move N Horizontally



In order to maximize angle C condider the following equations in terms of z

The resulting equation is A=arctan(3 tanB)

Since C=A-B, substituting A=arctan(3 tanB) we have C= arctan(3 tanB)-B.

To maximize C, we simply take the derivative of C= arctan(3 tanB)-B and set it equal to zero.

We can solve for B:

Keeping the relevant domain of B, (0,p/2), in mind, we find that when C is maximum B=p/6. Hence, to find the maximum viewing angle C= arctan(3 tanB)-B, simply substitute B=p/6 and evaluate .

So the maximum viewing angle is C=p/6

Determining the p/6 angle distance from G point

Since AGO is a 90 degree, angle we have

The angle we are seeking for is C, but we can see C=A-B, so we have :

We can look at the graph of C and z:


The tangent function:

we can find z that gives us a maximum C by setting the slope of tangent line of

then we get:

Simplifying the equation:







Labels: Picture height is PH and total height isTH

then we can write:

C=angle A-angle B

tan C=tan(A-B)=(tan A-tan B)/(1+tan B*tan A) then

we find the general formula

and then we get



In this problem

We would like to investigate the different ratios




Click Here to Move N Horizontally





Click Here to Move N Horizontally






Click Here to Move N Horizontally


We investigated most suitable angle for penalty kick


Click Here to Move B and D Horizontally



In Animation

We saw that somewhere between the 5 yard line and 2.5 yard line, the angle improves as the penalty is accepted.

As you can see below:the closer to the goal line, the greater the angle improvement.

 Name of the Angle  Degree of Agle


back to bio page