Yuki just bought a big screen TV set. The screen has a diagonal measure of 40 in. If the screen is 32 in. wide, how high is it?
a^2 + b^2 = c^2
32^2 + b^2 = 40^2
b^2 = 1600 - 1024
b^2 = 576
b = 24
Well, well, Yuki and her big screen TV! It sounds like she's ready to "diagonal-nose" dive into some quality entertainment. Now, to figure out the height of her TV, we can use a little bit of mathematical magic.
To do this, we'll need to call upon Pythagoras, the legendary Greek mathematician! According to his theorem, the square of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides.
In our case, the hypotenuse (diagonal) is 40 inches, and one of the sides (width) is 32 inches. So, we can create our equation:
40^2 = 32^2 + height^2
1600 = 1024 + height^2
To solve for height, we'll subtract 1024 from both sides:
height^2 = 576
Now, let me borrow my trusty calculator... (beep boop beep) The square root of 576 is 24.
So, the height of Yuki's big screen TV is 24 inches. Now, she can enjoy watching her favorite shows in larger-than-life fashion!
To find the height of the TV screen, we can use the Pythagorean theorem as follows:
Let the height of the TV screen be h.
According to the Pythagorean theorem,
(Length of diagonal)^2 = (Width)^2 + (Height)^2
Given:
Width (W) = 32 inches
Diagonal (D) = 40 inches
Plugging in the values:
(D)^2 = (W)^2 + (h)^2
(40)^2 = (32)^2 + (h)^2
Simplifying the equation:
1600 = 1024 + (h)^2
Subtracting 1024 from both sides:
(h)^2 = 576
Taking the square root of both sides:
h = √576
Simplifying the square root:
h ≈ 24 inches
Therefore, the height of the TV screen is approximately 24 inches.
To find the height of the TV screen, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the height of the TV screen is one of the sides in a right-angled triangle, with the width as the other side, and the diagonal as the hypotenuse.
1. First, let's label the sides of the triangle:
- Width (adjacent side) = 32 inches
- Height (opposite side, what we want to find) = ?
- Diagonal (hypotenuse) = 40 inches
2. We can use the Pythagorean theorem to solve for the height:
Diagonal^2 = Width^2 + Height^2
Substituting the known values:
40^2 = 32^2 + Height^2
3. Simplifying the equation:
1600 = 1024 + Height^2
4. Rearranging the equation by subtracting 1024 from both sides:
Height^2 = 576
5. Taking the square root of both sides to solve for height:
Height = √576
Height = 24 inches
Therefore, the height of the TV screen is 24 inches.