Where to sit at the movies

[SethW]

Hi I have a math lab that I have been working on and struggling to understand for the past few hours.


Hopefully these pictures can be enough of a help to visualize as well.

just to clarify I'm working on part (A)

the instructions from my instructor read

Hint: this is fairly complicated. Don't wait until the last minute. You'll want to draw lots of triangles to fiure out the various lengths. For starters, make a right triangle down from the base of the seat and mae a right triangle from the top of the screen horizontal to the left and then down to the head of the person in the seat. Use that to figure out the two legs of the bottom triangle (in terms of x) and then figure out the lengths of the two sides of the non-right triangle which includes (theta).


Problem 2 says

Now suppose that, starting with the first row of seats, the floor of the seating area is inclined a=25 degrees above the horizontal, and the distance that you sit up the incline is x, as shown in the figure.

a) Use the law of Cosines to show that

(1.) Theta=cos^-1((a^2+b^2-484)/(2ab))

(2.) A^2=(7+xcosa)^2+(28-xcosa)^2

and

(3.) B^2=(7+xcosa)^2+(xsina-6)^2

I have tried to understand how the numbers inside A^2 and B^2 relate to the depiction and the closest thing I can come up with is that they are removing four from both the distance from the floor to the screen and also from the entire distance from the floor to the top of the screen to account for the 4 feet increase from the floor of where you would sit to where your eyes are. From there I tried to write the equations in all different forms of its self.

I Plugged the a^2 and B^2 values in the equation 1 and I'm not sure where to go from there.

I have also drawn a depiction as my instructor has stated but I'm struggling with being able to write it in terms of x.

I know this is a complicated piece but please any help would be so greatly appreciated! Thank you!

 

[Deleted member 4993]

Hi I have a math lab that I have been working on and struggling to understand for the past few hours.
View attachment 4685View attachment 4686View attachment 4684

Hopefully these pictures can be enough of a help to visualize as well.

just to clarify I'm working on part (A)

the instructions from my instructor read

Hint: this is fairly complicated. Don't wait until the last minute. You'll want to draw lots of triangles to fiure out the various lengths. For starters, make a right triangle down from the base of the seat and mae a right triangle from the top of the screen horizontal to the left and then down to the head of the person in the seat. Use that to figure out the two legs of the bottom triangle (in terms of x) and then figure out the lengths of the two sides of the non-right triangle which includes (theta).


Problem 2 says

Now suppose that, starting with the first row of seats, the floor of the seating area is inclined a=25 degrees above the horizontal, and the distance that you sit up the incline is x, as shown in the figure.

a) Use the law of Cosines to show that

(1.) Theta=cos^-1((a^2+b^2-484)/(2ab))

(2.) A^2=(7+xcosa)^2+(28-xcosa)^2

and

(3.) B^2=(7+xcosa)^2+(xsina-6)^2

I have tried to understand how the numbers inside A^2 and B^2 relate to the depiction and the closest thing I can come up with is that they are removing four from both the distance from the floor to the screen and also from the entire distance from the floor to the top of the screen to account for the 4 feet increase from the floor of where you would sit to where your eyes are. From there I tried to write the equations in all different forms of its self.

I Plugged the a^2 and B^2 values in the equation 1 and I'm not sure where to go from there.

I have also drawn a depiction as my instructor has stated but I'm struggling with being able to write it in terms of x.

I know this is a complicated piece but please any help would be so greatly appreciated! Thank you!

Did you notice: 22² = 484

and

Do you know the "Law of cosines" of a triangle?