Question

Find the angle between a diagonal of a cube and one of its edges. (Round your answer to the nearest degree.

Answer 1

Answer:

The angle between the diagonal and edge = 55 degrees

Explanation:

We will find it by finding the angle between two vectors (a and b)

We will assume it to be a unit cube

Vector a = (1,1,1)      (defines the diagonal vector)

Vector b = (1,0,0)    (defines the edge vector)

cos (theta) = (a.b)/(|a|*|b|)

$cos (theta) = 1 / (\sqrt{3} * \sqrt{1}  )$

theta = 54.74 degrees

theta = 55 degrees (Rounded to the nearest degree)

Answer 2

The angle between a diagonal of a cube and one of its edges is 55° to the nearest degree

Diagonal and edge of a cube

• The diagonal of a cube is a segment joining two points that are not the endpoints of an edge.
• An edge of a cube is a line segment joining the two vertices

Assuming the length of a side of the cube is 1.

The 3 sides are given by the vectors:

• a = (1,0,0)
• b = (0,1,0)
• and c = (0,0,1)

Each produces the same angle.

Then the diagonal is given by the vector v = (1,1,1)

Solving for angle between diagonal and one edge of the cube

cos θ = v.a/|v|.|a|

cos θ = 1/√3

θ =( 1/cos) 1/√3

θ = 55° to the nearest degree

Therefore, the angle between a diagonal of a cube and one of its edges is 55° to the nearest degree

Learn more about diagonal and edge of cubes at: https://brainly.com/question/10368457