Answer:
1. 143.95 feet
2. 106.5 feet.
Step-by-step explanation:
Diagram: Attachment
Calculations:
Length of the guy-wire (AC):
In order to find the length of the guy-wire, we can use the sine function. The sine of an angle is equal to the ratio of the length of the opposite side to the hypotenuse.
In this case, the opposite side is the height of the pole (h feet) and the hypotenuse is the length of the guy-wire (AC).
We can set up the equation:
sin(46°) = h / AC
cos(46°) = 100/ AC
AC=100/cos(46°)
AC=143.95
the guywire is 143.95 ft.
For height of pole:
Sin(46°)=h/AC
Rearranging the equation, we can solve for AC:
AC = h / sin(46°)
143.95=h/ sin(46°)
sin(46°)*144=h
h=103.5ft
Now height of pole:
h+3=103.5+3
h=106.5 ft
Step-by-step explanation:
To find the length of the guy-wire, we used the sine function. We set up the equation sin(46°) = h / AC, where h+3 represents the height of the pole. Rearranging the equation, we solved for AC and found it to be approximately 143.95 feet.
To find the height of the pole, we used the cosine function. We set up the equation cos(46°) = 100 / AC and rearranged it to solve for h. We found that h is approximately 106.5 feet.
Therefore, the length of the guy-wire is approximately 143.95 feet, and the height of the pole is approximately 106.5 feet.