A tower is supported by a guy wire from the top of the tower to the ground 16 ft from its base. The

wire makes an angle of 62 with the ground. The length of the wire is

a. 30.09 ft
b. 18.12 ft
c. 28.41 ft
d. 34.08 ft

cos 62 = 16/L

L = 16 / cos 62 = 34.08

To find the length of the wire, we can use the trigonometric relationship of the angle and the sides of a right triangle. In this case, the guy wire forms a right triangle with the ground and the tower, where the angle is 62 degrees.

Let's label the sides of the triangle:
- The length of the wire is the hypotenuse of the triangle.
- The distance from the base of the tower to the point where the guy wire meets the ground is the adjacent side.
- The height of the tower is the opposite side.

Using the cosine function:
cos(angle) = adjacent/hypotenuse

In this case:
cos(62) = 16/hypotenuse

Now we can solve for the hypotenuse (length of the wire):
hypotenuse = 16/cos(62)

Calculating the value:
hypotenuse ≈ 30.09 ft

Therefore, the length of the wire is approximately 30.09 ft.

Hence, the correct answer is option a. 30.09 ft.