Answer:
Approximately, there is a distance of 25,6 foot between the base of the flagpole to the house.
Step-by-step explanation:
We are given the following in the question:
Height of pole = 20 foot
Angle between pole and ground = 85 degrees
Angle of elevation from the base of the house to the top of the pole = 55 degrees
Then, the third angle of the triangle can be found as:
Angle sum property of triangle: The sum of the three angles of a triangle is 180 degrees.

Thus, by the sin rule, we can write:

Approximately, there is a distance of 25,6 foot between the base of the flagpole to the house.