Question

To manufacturing floor

T
30 in.
72 in.
to loading dock
D
48 in.
36 in.
g) What is the longest rod that can be carried to the loading dock? Round to
the nearest tenth of an inch.

Answer 1

To determine the longest rod that can be carried to the loading dock, we want to find the shortest distance from point T to line segment CD. We can use the Pythagorean theorem for this.

First, we need to find the equation of the line containing segment CD. We can find the slope of the line CD as:

m = (y2 - y1) / (x2 - x1) = (36 - 48) / (48 - 0) = -12/48 = -1/4

where (x1, y1) = (0, 48) and (x2, y2) = (48, 36).

Using point-slope form, we get the equation of the line CD as:

y - 48 = (-1/4)(x - 0)

y = (-1/4)x + 48

Now, we can find the perpendicular distance from point T to the line CD as follows:

d = |(-1/4)(30) + 72 - 48| / sqrt((-1/4)^2 + 1)

d = 42 / sqrt(17) ≈ 10.21

Therefore, the longest rod that can be carried to the loading dock is approximately 10.2 inches long (rounded to the nearest tenth of an inch).