Question

Danica is in the observation area of the sears tower in chicago overlooking lake michigan. She sights two sailboats going due east from the tower. The angles of depression to the two boats are 42 degrees and 29 degrees. If the observation deck is 1,353 feet high, how far apart are the boats?

Answer 1

Answer:

The boats are far apart by 4506.1 feet

Step-by-step explanation:

from the graph attached

i) BC = 1353 $\times tan(71\textdegree)$ = 2761.82 feet

ii) BD  = 1353 $\times tan(58\textdegree)$ =  1744.28 feet

iii) the boats are far apart by = CD = CB + BD = 2761.82 + 1744.28 = 4506.1 feet