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