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A 238 ft tower is located on the side of a
mountain that is inclined 38° to the horizontal. A
guy wire is to be attached to the top of the tower
and anchored at a point 50 ft downhill from the
base of the tower. Find the shortest length of
wire needed.
50 ft
38°
238 ft
NOTE: The picture is NOT drawn to scale.
length of guy-wire =
ft
Enter your answer as a number; your answer
should be accurate to 2 decimal places.

A 238 ft tower is located on the side of a mountain that is inclined 38 to the horizontal A guy wire is to be attached to the top of the tower and anchored at a class=

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itzamirv2

To find the shortest length of the guy-wire, we'll use trigonometry. The guy-wire forms the hypotenuse of a right triangle, where the tower's height is one leg and the distance from the tower's base to the anchoring point is the other leg.

Given:

- The height of the tower h = 238 ft

- The distance from the base of the tower to the anchoring point downhill d = 50 ft

- The angle of inclination θ = 38 degrees

We can use the trigonometric relationship of sine to find the length of the guy-wire g:

sin(θ) = h / g

First, let's find the height of the tower above the anchoring point. This can be calculated using the sine function:

h = g * sin(θ)

Rearranging for g:

g = h / sin(θ)

Substituting the given values:

g = 238 / sin(38 degrees)

Calculating:

g ≈ 238 / 0.6157 ≈ 386.14 ft

So, the shortest length of the guy-wire needed is approximately 386.14 ft.

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