Problema Solution
the base of a ten foot ladder is 6 feet from a building. The top of the leaning ladder reaches and makes contact with the buildings roof. On the corner of the building, a 4 foot flag pole is erected on the roof. A spot light with a fixed angle of elevation of 57 degrees is to be permanently secured to the ground and aimed to shine on the top of the flagpole. Determine how many feet from the corner of the building to place the spotlight.
Answer provided by our tutors
First, using the Pythagorean Theorem we find the height of the building:
H^2 = 10^2 - 6^2
H^2 = 64
H = 8 ft
Now we use trigonometry to find the distance of the spotlight to the building:
tan(57) = (4 + 8)/x
x = 12/tan(57)
x = 7.79 ft
The spotlight should be placed 7.79 feet from the building.