Answer:
The Pole is 76.05 feet tall.
Step-by-step explanation:
The perpendicular height of the pole from the ground forms a right angled triangle with pole and the ground and another right angled triangle with the cable and the ground.
Let the perpendicular distance be x and distance from the bottom of this distance to the bottom of the pole be y feet, we have:
tan 65 = x/y
tan 40 = x / ( y + 50)
From the first equation, x = y tan 65 so
tan 40 = y tan 65 / (y + 50)
y tan 65 = y tan40 + 50 tan40
y ( tan65 - tan 40) = 50 tan 40
y = 50 tan40 / (tan 65 - tan 40)
y = 32.14 feet
and x = 32.14 * tan65
= 68.92 feet.
By Pythagoras the height of the pole = √ (68.92^2 + 32,14^2)
= 76.05 feet.
