1. Television screens are sized according to the length of a diagonal across the screen, from one corner to another. The screen of a 2 inch wide screen TV is 24.5 inch high. How wide is it?
2. A carpenter needs to build a stairway down to a basement in a house under construction. The vertical drop is 8'9" and in order to keep the staircase from being too steep it will extend 14 feet horizontally. The main supports will go diagonally from he top of the stairs to the basement floor. How long do they need to be?
1. 2-inch wide screen? Are you sure?
2. Use the Pythagorean Theorem.
https://www.mathsisfun.com/pythagoras.html
screen is 52 inches
Use the Pythagorean Theorem.
http://www.mathsisfun.com/pythagoras.html
1. To find the width of the TV screen, we can use the Pythagorean theorem (a^2 + b^2 = c^2) since we know the height and the diagonal.
Let's assign variables:
- Let's say the width of the TV screen is 'w' inches.
- The height of the TV screen is given as 24.5 inches.
- The diagonal length is given as 2 inches.
Using the Pythagorean theorem, we can write the equation as:
w^2 + 24.5^2 = 2^2
Simplifying the equation:
w^2 + 600.25 = 4
Rearranging the equation:
w^2 = 4 - 600.25
w^2 = -596.25
Since the width cannot be negative, we can conclude that there is no real solution for the width of the TV screen given the provided information.
2. To find the length of the main supports needed for the staircase, we can use the Pythagorean theorem (a^2 + b^2 = c^2) since we know the vertical drop and the horizontal extension.
Let's assign variables:
- Let's say the vertical drop is 'a' (8 feet 9 inches = 8.75 feet).
- The horizontal extension is 'b' (14 feet).
- The length of the main supports (diagonal length) is 'c'.
Using the Pythagorean theorem, we can write the equation as:
a^2 + b^2 = c^2
Substituting the given values:
(8.75)^2 + (14)^2 = c^2
Simplifying the equation:
76.5625 + 196 = c^2
272.5625 = c^2
Taking the square root on both sides of the equation:
c = sqrt(272.5625)
c ≈ 16.51 feet
Therefore, the main supports needed for the staircase should be approximately 16.51 feet long.