A31 foot support wire is attached from the top of a 25 foot telephone pole to a point on the ground how far from the poles base does the wire meet the ground

You have a right triangle here with the length of the hypotenuse as 31 and the vertical leg as 25. In order to find the length of the base leg, you need one of the angle measures. Let's find the measure of the other base angle using the sin ratio: sin A = 25/31. sin A = .8064516, and sin^-1(.8064516)=53.75. So the other base angle measures 53.75 degrees. Now use that angle and the cos ratio to find the length of the missing leg. cos(53.75)=x/31. x = 31 cos(53.75), and x = 18.33