a tether is tied tautly to the top of a pole as shown. what is the slope of the tether

Question

the tether is 9ft tall and the line goes out 12ft

 

Answer 1

Hi Meghan:

 

I don't see a drawing, but let us say the pole is 9 feet tall and the line which holds the top to the ground is 12 feet long (if those assumptions are incorrect, you can follow the same procedure with the correct numbers).

 

The pole and the horizontal ground form a 90o right angle.  Therefore, you can calculate the projection of the line on the ground by using the square rule:  a^2 + b^2 = c^2;  The horizontal side of the right triangle is then:

a^2 = c^2 - b^2 = 12x12 - 9x9 = 63;

 

now take the square root to get:

a = 7.94 (very close to 8).

 

The slope of the line is now:  (difference in y coordinate) divided by (difference in x coordinate) = pole height / a

Slope = 9 / 7.94 = 1.133

 

The slope is greater than 1.0, it means that the angle of the line from the ground is more than 45o.

 

Hope this helps!

 

  Jean-Michel