As shown in the diagram, the height of building AB is 100 feet. The height of building CD is 50 feet. The buildings are on opposite sides of an avenue that is 90 feet wide. From a point E on the avenue, the measure of the angle of elevation to B is 55º. Determine the distance from E to D to the nearest foot.

Question

anonymous · Answer

Use primary trig ratios to begin with.

anonymous · Answer

sin 55 = 100/EB

anonymous · Answer

EB = 122.077 ft

anonymous · Answer

Now, find the distance from a to e by using trig ratios again: cos 55 = ae/ 122.077, 13 = 70.02. This means that EC is 19.979

anonymous · Answer

Now, we can calculate the angle of elevation for ED: tan x = 50/19.979, x =68.219 degrees.

anonymous · Answer

With that, one more use of trig ratios gives us sin 68.219 = 50/ED, ED =53.8429

anonymous · Answer

Thus, the distance from E to D is 54 ft.