SOLUTION: The angle of depression of boat A from the tip of a cliff which measures 32m is 24deg 16 min, while boat B from the same point measures 18deg 12min angle of depression. FIND THE DI

Algebra ->  Triangles -> SOLUTION: The angle of depression of boat A from the tip of a cliff which measures 32m is 24deg 16 min, while boat B from the same point measures 18deg 12min angle of depression. FIND THE DI      Log On


   

Question 1016477: The angle of depression of boat A from the tip of a cliff which measures 32m is 24deg 16 min, while boat B from the same point measures 18deg 12min angle of depression. FIND THE DISTANCE BETWEEN BOAT A AND B.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The angle of depression of boat A from the tip of a cliff which measures 32m is 24deg 16 min, while boat B from the same point measures 18deg 12min angle of depression.
FIND THE DISTANCE BETWEEN BOAT A AND B.
:
Change 24 deg 16 min to 24.267 degrees (divide 16 by 60)
Change 18 deg 12 min to 18.2 degrees
:
Draw this out. We can see two right triangle, one for each boat
:
Boat A
The interior angle: 90 - 24.267 = 65.733 degrees
The distance (d) from the base of the cliff to Boat A is the side opposite 65.733 deg
Tan(65.733) = d%2F32
d = 32 * 2.218
d = 70.98 m to Boat A
:
Boat B
The interior angle: 90 - 18.2 = 71.8 degrees
The distance (d) from the base of the cliff to Boat B is the side opposite 71.8 deg
Tan(71.8) = d%2F32
d = 32 * 3.04
d = 97.33 m to Boat B
:
Find the distance between them
97.33 - 70.98 = 26.35 meters between Boat A & B