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Look out for the
rocks!Application of Trigonometry
by Pete Anderson
Web Source
Did you know . . .
… the Lighthouse of Alexandria was one of the Seven Wonders of the Ancient World?
Problem:If a ship can spot the top of a lighthouse at an angle of elevation of 10° and the height of the lighthouse is know to be 150 feet above sea level, then how far from the lighthouse is the ship?
Create a DiagramIf a ship can spot the top of a lighthouse at an angle of elevation of 10° and the height of the lighthouse is known to be 150 feet above sea level, then how far from the lighthouse is the ship?
10°
X150feet
Writing an Equation
10°
X
150
150tan10
x
SOH
CAH
T
pneumonic
OA
OH A
sin
cos
tan
Solving the Equation
150tan10
x 150
0.1763x
0.1763 150x
150
0.1763x
850.8x feet
150tan10
x
Verify Your Solution
10°
X
150
850.8150
tan10x
850.8x feet
o 150tan10 =
850.8
0.1763 0.1763
Quiz
If a lighthouse keeper spots a ship at an angle of depression of 12° and the height of the lighthouse is know to be 175 feet above sea level, then how far from the lighthouse is the ship?
A. 37 feetB. 179 feetC. 823 feetD. 842 feet
Solution to Quiz
12°
X
175feet
12°
o 175tan12 =
x175
0.2126
0.2126 175
175
0.2126823.1
xx
x
x feet
o 175tan12 =
x
823.1x feet
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