SOLUTION: In a museum of​ art, the most intriguing piece is a line of red yarn 22.05 ft long that dissects the​ room, drawing the eye up and out the window. It extends from point

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: In a museum of​ art, the most intriguing piece is a line of red yarn 22.05 ft long that dissects the​ room, drawing the eye up and out the window. It extends from point      Log On


   

Question 1102012: In a museum of​ art, the most intriguing piece is a line of red yarn 22.05 ft long that dissects the​ room, drawing the eye up and out the window. It extends from point x in the floor of the room to point y in the window 8.7 ft from the floor. How far is point x from point z at the bottom of the window directly below point​ y?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the yarn forms right triangle xyz where:

xy is the hypotenuse.
yz is the vertical side.
xz is the horizontal side.

you are given that xy is equal to 22.05 and yz is equal to 8.7.
xz is what you want to find.

the pythagorus formula for a right triangle states that c^2 = a^2 + b^2

c is the hypotenuse and a and b are legs of the right triangle.

let xy = c and let yz = a and let xz = b and the formula becomes:

22.05^2 = 8.7^2 + b^2

solve for b^2 to get b^2 = 22.05^2 - 8.7^2 = 410.5125

solve for b to get b = sqrt(410.5125) = 20.26110806

since b = xz, then xz = 20.26110806 also.

that's the horizontal distance from where the point where the string starts to the point when it intersects with the window.