And They Lived Happily Ever After

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And They Lived Happily Ever After

• Application of Trigonometry
• by Amy Au

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Did you know

• that Princess Elizabeth was locked inside the
  Tower of London for eight weeks!

Web source
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Problem

• If prince charming looks up at the princesss
  tower at an angle of elevation of 40 and he is
  120 feet from the base of the tower, then how far
  up would he have to climb to reach the top?

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If prince charming looks up at the princesss
tower at an angle of elevation of 40 and he is
120 feet from the base of the tower, then how far
up would he have to climb to reach the top?
Create a Diagram
X
40
120 feet
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Tan 40
Writing an Equation
pneumonic SOH sin CAH cos TOA tan
O
H
X
40
A
120 feet
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Tan 40
Solving the Equation
0.839
X 0.839(120)
X 100.6919 feet
100.7 feet
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Verify Your Solution

• 100.7 feet

Tan 40
0.839 0.839
X
X 100.7
40
120 feet
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Quiz

• If the princess is looking down at prince
  charming from an angle of depression of 65 and
  he is 90 feet away from the base of the tower,
  then how far up would he have to climb to reach
  her?

A. 193.0 feet B. 38.03 feet C. 81.567 feet D.
83.92 feet
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Solution to Quiz
Tan 65
2.1445

• Tan 65

X 193.0
193.0 feet
65
x
65
90 feet