Answer:
All answers are to 2 decimal places for accuracy.
1. Width is 27.71"
2. TV Size is 69.84"
3. Width is 51.96"
4. TV Size is 40.13"
5. Height is 26.06"
6.
Part 1: Diagonal is 61.91"
Part 2: Diagonal is 60.21"
Step-by-step explanation:
THe pythagorean theorem tells us that the sum of two legs of a triangle squared equal the hypotenuse squared.
Note: This applies for right triangles and the side opposite of the right angle is the hypotenuse
Also, to solve the first 5 problems, we can say:
[tex]Height^2 + Width^2 = TV \ Size^2[/tex]
#1 32” TV height: 16” width: _____
Let width be w
[tex]16^2 + w^2 = 32^2\\w =\sqrt{32^2 - 16^2} \\w=27.71[/tex]
Width is 27.71"
#2 _____ TV height: 34” width: 61”
Let tv size be t
[tex]34^2 + 61^2 = t^2\\t= \sqrt{34^2 + 61^2} \\t=69.84[/tex]
TV Size is 69.84"
#3 60” TV height: 30” width: _____
Let width be w
[tex]30^2 + w^2 = 60^2\\w =\sqrt{60^2 - 30^2} \\w=51.96[/tex]
Width is 51.96"
#4 _____ TV height: 20” width: 35”
Let tv size be t
[tex]20^2 + 35^2 = t^2\\t= \sqrt{20^2 + 35^2} \\t=40.31[/tex]
TV Size is 40.13"
#5 52” TV height: _____ width: 45”
Let height be h
[tex]h^2 + 45^2 = 52^2\\h =\sqrt{52^2 - 45^2} \\h=26.06[/tex]
Height is 26.06"
#6
Part1:
New dimensions would be
48+5 = 53" Width
27+3 = 30" Height
Let diagonal be d, so
[tex]d=\sqrt{53^2+32^2} \\d=61.91[/tex]
Diagonal is 61.91"
Part 2:
New dimensions are:
48+3 = 51" Width
27 + 5 = 32" Height
Let diagonal be d, so
[tex]d=\sqrt{51^2+32^2} \\d=60.21[/tex]
Diagonal is 60.21"
