Suppose each edge of the cube shown in the figure is x inches long. find the sine and cosine of the angle formed by diagonals cf and ch.

 The answer is  

Step-by-step explanation:  Given in the question that ABCDEFGH is a cube with edge length 'x' inches. We need to find the sine and cosine of the angle formed by the diagonals CF and CH.

As shown in the attached figure, we cut ΔCFH from the cube, which is a right-angled triangle at ∠CHF=90°. Let, ∠FCH = α.

Now, we need to find the sine and cosine of α.

Since each side of a cube is a square, so CDHG is a square and CH is its diagonal. So,

Again, from right-angled triangle CFH, we have

Therefore,

and

Thus, the answer is

answer: this is not a question

step-by-step explanation: this is a answer

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240