)a rectangular box has length 12 inches, width 20 inches, and a height of 7 inches. find the angle between the diagonal of the box and the diagonal of its base. the angle should be measured in radians.

We assume the base is 12 in × 20 in, so its diagonal has length

... √(12² +20²) = √(144 +400) = √544 = 4√34 . . . inches

Then the tangent of the angle of interest is the ratio of the box height to the base diagonal:

... tan(α) = (7 in)/(4√34 in) ≈ 0.300123

The angle will be the arctangent of this value,

... α = arctan(7/√544) ≈ 0.291569 radians

17

step-by-step explanation:

step-by-step explanation: given equation a = h(b 1+b 2)

also we are given values of a, h and b 1 as :

a = 16, h = 4, and b 1 = 3.

in order to solve it for b 2, we need to plug the given values of   a, h and b 1 .

therefore, plugging values of   a, h and b 1   in given equation, we get

16 = 4( 3 + b 2)

first dividing both sides by 4, we get

4 = 3 + b 2

subtracting 3 from both sides, we get

4 -3 = 3 -3 + b 2

1 = b 2.