Pothagorem therom

Determine the missing measurements for each TV.

32” TV height: 16” width: _____

• _____ TV height: 34” width: 61”

• 60” TV height: 30” width: _____

• _____ TV height: 20” width: 35”

• 52” TV height: _____ width: 45”

If a TV has the following dimensions 48” wide, 27” height, and 55”diagonal. Respond to the following questions.

If the TV is 5” wider and 3” higher, what is the new diagonal measurement? (Show work)

 If the TV is 3” wider and 5” higher, what is the new diagonal measurement? (Show work)

In all your cases, it appears that TV represents the diagonal of the television.

In all cases, PYTHAGORAS, (notice the spelling), says

TV^2 = height^2 + width^2

just insert the 2 given data values, and solve for the missing one

I will do one, you do the others in the same way:
• 60” TV height: 30” width: _____
TV^2 = height^2 + width^2
60^2 = 30^2 + width^2
3600 = 900 + width^2
2700 = width^2
width^2 = √2700 = appr 52 inches

To determine the missing measurements for each TV, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

For example, let's solve for the missing width in the first TV.

Given:
32” TV height: 16” width: _______

Using the Pythagorean theorem, we have:

Width^2 + Height^2 = Hypotenuse^2

Substituting the given values:

Width^2 + 16^2 = 32^2

Width^2 + 256 = 1024

Width^2 = 1024 - 256

Width^2 = 768

Taking the square root of both sides:

Width = √(768)

Width ≈ 27.7 inches (rounded to one decimal place)

So, the missing width for the first TV is approximately 27.7 inches.

Similarly, we can calculate the missing measurements for the other TVs using the same method:

• _____ TV height: 34” width: 61”

Applying the Pythagorean theorem:

Width^2 + 34^2 = Hypotenuse^2
Width^2 + 1156 = Hypotenuse^2

The answer is undefined because we are missing the required information to find the width of this TV.

• 60” TV height: 30” width: _____

Applying the Pythagorean theorem:

Width^2 + 30^2 = Hypotenuse^2
Width^2 + 900 = Hypotenuse^2

The answer is undefined because we are missing the required information to find the width of this TV.

• _____ TV height: 20” width: 35”

Applying the Pythagorean theorem:

Width^2 + 20^2 = Hypotenuse^2
Width^2 + 400 = Hypotenuse^2

The answer is undefined because we are missing the required information to find the width of this TV.

• 52” TV height: _____ width: 45”

Applying the Pythagorean theorem:

Height^2 + 45^2 = Hypotenuse^2
Height^2 + 2025 = Hypotenuse^2

The answer is undefined because we are missing the required information to find the height of this TV.

For the TV with the dimensions 48” wide, 27” height, and 55” diagonal, let's answer the following questions:

If the TV is 5” wider and 3” higher, what is the new diagonal measurement?

Given:
Width = 48 + 5 = 53 inches (increased by 5 inches)
Height = 27 + 3 = 30 inches (increased by 3 inches)

To find the new diagonal measurement, we can use the Pythagorean theorem:

Width^2 + Height^2 = Diagonal^2
53^2 + 30^2 = Diagonal^2

Diagonal^2 = 2809 + 900
Diagonal^2 = 3709

New Diagonal = √(3709)
New Diagonal ≈ 60.94 inches (rounded to two decimal places)

Therefore, the new diagonal measurement for the TV, if it is 5 inches wider and 3 inches higher, is approximately 60.94 inches.

Similarly, for the second question:

If the TV is 3” wider and 5” higher, what is the new diagonal measurement?

Given:
Width = 48 + 3 = 51 inches (increased by 3 inches)
Height = 27 + 5 = 32 inches (increased by 5 inches)

Using the Pythagorean theorem:

Width^2 + Height^2 = Diagonal^2
51^2 + 32^2 = Diagonal^2

Diagonal^2 = 2601 + 1024
Diagonal^2 = 3625

New Diagonal = √(3625)
New Diagonal ≈ 60.21 inches (rounded to two decimal places)

Therefore, the new diagonal measurement for the TV, if it is 3 inches wider and 5 inches higher, is approximately 60.21 inches.

To determine the missing measurements for each TV, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

For the first set of missing measurements, where we know the height is 16 inches and need to find the width for a 32-inch TV:

We can set up a right triangle where the height is one side (16 inches) and the width is the other side (unknown), and the hypotenuse is the diagonal (32 inches). According to the Pythagorean theorem:

width^2 + height^2 = diagonal^2

Plugging in the known values:

width^2 + 16^2 = 32^2

width^2 + 256 = 1024

Subtracting 256 from both sides:

width^2 = 768

Taking the square root of both sides:

width = √768
width ≈ 27.7 inches

Therefore, the missing width measurement for the 32” TV is approximately 27.7 inches.

We can follow a similar process for the remaining sets of missing measurements. Here are the solutions for each:

• For a TV with a height of 34 inches and width of 61 inches:

width^2 + 34^2 = diagonal^2

width^2 + 1156 = diagonal^2

width = √(diagonal^2 - 1156)

So, the missing width measurement cannot be determined without knowing the diagonal measurement.

• For a 60” TV with a height of 30 inches and missing width:

width^2 + 30^2 = diagonal^2

Missing width = √(diagonal^2 - 900)

However, we cannot determine the missing width without knowing the diagonal measurement.

• For a TV with a height of 20 inches and width of 35 inches:

35^2 + 20^2 = diagonal^2

diagonal^2 = 1225 + 400

diagonal = √1625
diagonal ≈ 40.3 inches

Therefore, the missing diagonal measurement for the TV is approximately 40.3 inches.

• For a TV with a width of 45 inches and a missing height:

45^2 + height^2 = diagonal^2

Missing height = √(diagonal^2 - 2025)

However, we cannot determine the missing height without knowing the diagonal measurement.

Now, let's answer the additional questions:

For a TV with dimensions 48” wide, 27” high, and 55” diagonal:

1. If the TV is 5” wider and 3” higher, we need to find the new diagonal measurement.

New width = 48 + 5 = 53 inches
New height = 27 + 3 = 30 inches

Applying the Pythagorean theorem:

53^2 + 30^2 = new diagonal^2

New diagonal = √(53^2 + 30^2)
New diagonal ≈ 61.8 inches

The new diagonal measurement is approximately 61.8 inches.

2. If the TV is 3” wider and 5” higher:

New width = 48 + 3 = 51 inches
New height = 27 + 5 = 32 inches

Applying the Pythagorean theorem:

51^2 + 32^2 = new diagonal^2

New diagonal = √(51^2 + 32^2)
New diagonal ≈ 60.5 inches

The new diagonal measurement is approximately 60.5 inches.

wth. y did they have to complicate something so simple. idiots

Im confused?

JUST ANSWER THE F'ING QUESTION!!!!!!!