32” TV height: 16” width: _____
32^2 + 16^2=
=1024 + 256
=1280
c = 35
• _____ TV height: 34” width: 61”
a^2+b^2
34^2 + 61^2
=1156 + 3721
=4877
c = 69
• 60” TV height: 30” width: _____
a^2 + b^2
=60^2 + 30^2
=3600 + 900
=4500
= 67
• _____ TV height: 20” width: 35”
a^2 + b^2
20^2 + 35^2
=400 + 1225
=1625
=40
• 52” TV height: _____ width: 45”
a^2 + b^2
52^2 + 45^2
=2704 + 2025
=4729
= 68
its kinda confusing Mrs Reiny
No, you are simply using the two given numbers in each question as if they always represented the length and width.
That happened to work in #2 and #4, but the others are wrong.
The size of TV's is measured in terms of its diagonal, so Pythagoras would say:
T^2 = L^2 + W^2
So in each case you have to sub into the matching variable
e.g. #1
given: T = 32, W = 16, so
32^2 = L^2 + 16^2
1024 = L^2 + 256
768 = T^2
T = √768 = appr 28
(You had 35, how can the width be more than the diagonal??)
how can i fix it
How can you fix it??
Did you not read my reply and the example I gave you?
t^2 = diagonal^2 = length^2 + width^2
That is what Reiny is telling you
so
length^2 = diagonal^2 - width^2
and
width^2 = diagonal^2 - length^2
To find the missing width in the given TV sizes, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's go through each TV size one by one:
1. For the 32" TV with a height of 16", we can find the missing width by using the Pythagorean theorem:
Width^2 = 32^2 - 16^2
Width^2 = 1024 - 256
Width^2 = 768
Width ≈ √768
Width ≈ 27.7"
2. For the TV with a height of 34" and a width of 61", we can calculate the missing side using the Pythagorean theorem:
Width^2 = 34^2 + 61^2
Width^2 = 1156 + 3721
Width^2 = 4877
Width ≈ √4877
Width ≈ 69"
3. For the 60" TV with a height of 30", we can apply the Pythagorean theorem:
Width^2 = 60^2 - 30^2
Width^2 = 3600 - 900
Width^2 = 2700
Width ≈ √2700
Width ≈ 51.96" (rounded to 52")
4. For the TV with a height of 20" and a width of 35", we use the Pythagorean theorem:
Width^2 = 20^2 + 35^2
Width^2 = 400 + 1225
Width^2 = 1625
Width ≈ √1625
Width ≈ 40.31" (rounded to 40")
5. Finally, for the 52" TV with a width of 45", we find the missing height:
Height^2 = 52^2 - 45^2
Height^2 = 2704 - 2025
Height^2 = 679
Height ≈ √679
Height ≈ 26.07" (rounded to 26")
These calculations provide the missing width or height for each TV size using the Pythagorean theorem.