Question

Draw a big diagram

You end up with a triangle with:

the horizontal side = 47 ft

the side representing the leaning pole ... call it a

and the angle opposite the pole side = 51°



The pole makes an angle of 7° with the vertical ... so the angle between to pole side and the 47ft side = 90 - 7 = 83°

So that make the angle opposite the 47 ft side = 180 - (51 + 83) = 46°


Now you can use the sine rule to find the length of the pole:

a/sin51° = 47/sin46

a = 47 * sin51 / sin46

a = 50.8 ft

so the length of the pole is 50.8 ft