Answer:
Step-by-step explanation:
Use the half angle identity for cosine:
cos(x/2)=+ or - sqrt(1+cos(x))/sqrt(2)
I'm going to figure out the sign part first for cos(x/2)...
so x is in third quadrant which puts x between 180 and 270
if we half x, x/2 this puts us between 90 and 135 (that's the second quadrant)
cosine is negative in the second quadrant
so we know that
cos(x/2)=-sqrt(1+cos(x))/sqrt(2)
Now we need cos(x)... since we are in the third quadrant cos(x) is negative...
If you draw a reference triangle sin(x)=3/5 you should see that cos(x)=4/5 ... but again cos(x)=-4/5 since we are in the third quadrant.
So let's plug it in:
cos(x/2)=-sqrt(1+4/5)/sqrt(2)
No one likes compound fractions (mini-fractions inside bigger fractions)
Multiply top and bottom inside the square roots by 5.
cos(x/2)=-sqrt(5+4)/sqrt(10)
cos(x/2)=-sqrt(9)/sqrt(10)
cos(x/2)=-3/sqrt(10)
Rationalize the denominator
cos(x/2)=-3sqrt(10)/10
The area of a square is (side)².
If the area is 128m², then the side is (√128) meters. (That's 8√2.)
The diagonal is the hypotenuse of the right triangle you get
if you slice the square in half along the diagonal. Its length is
given in the words of Old Pythagoras:
c² = a² + b²
'a' and 'b' are sides of the square, so
c² = (√128)² + (√128)²
= 2 (√128)²
c = √ (2 x 128) = √256 = 16 meters .
In the above word problem, If she chooses the 8-inch tiles, she will need a quarter as many tiles as she would with 2-inch tiles, Quarter 8-inch tiles will cover the same area as one 2-inches.
<h3>What is the justification for the above?</h3>
Note that the area of the one 2-inch tiles is given as:
A1 = 4in²
The area of the quarter 8-inch tiles is:
A2 = 1/4 x 8 x 8
A2 = 16inch²
Divide both areas
A2/A1= 16/4
= 4
This implies she'll need four 2-inch tiles to cover the same amount of space as a quarter 8-inch tile.
Learn more about word problems:
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Full Question:
A homeowner is deciding on the size of tiles to use to fully tile a rectangular wall in her bathroom that is 80 inches by 40 inches. The tiles are squares and come in three side lengths: 8 inches, 4 inches, and 2 inches. State if you agree with each statement about the tiles. Explain your reasoning.
If she chooses the 8-inch tiles, she will need a quarter as many tiles as she would with 2-inch tiles,
Step-by-step explanation:
∠4 = ∠1 & ∠2 = ∠3
360 - 2(98) = ∠2 + ∠3
∠3 = 164/2
∠3 = 82°
