The broken part will form the hypotenuse of a right triangle...call this x
And we know an angle and an adjacent side [19] to this angle.....
So.....the trig relationship that best describes this is the cosine.....so
cos 75 = 19 / x rearrange
x = 19 / cos 75 = about 73.41 ft
And the height of the standing part, h, can be found by the tangent.....so we have
tan 75 = h / 19
h = 19 * tan 75 = about 70.91 ft
The total height of the pole is the sum of these = 73.41 + 70.91 = about 144.32 ft
