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A statue is mounted on top of a 42 foot hill. From the base of the hill to where you are standing is 73 feet and the statue subtends an angle of 10.3° to where you are standing. Find the height of the statue.

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sqdancefan

Answer:

  19.72 ft

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relation between angles and sides of a right triangle:

  Tan = Opposite/Adjacent

Then the relations in the attached drawing are ...

  tan(α) = 42/73

  tan(α +10.3°) = (42 +SH)/73

Solving the first equation for α, we get ...

  α = arctan(42/73)

Solving the second equation for SH, we get ...

  73 tan(α +10.3°) = 42 +SH

  SH = 73·tan(arctan(42/73) +10.3°) -42 = 73·tan(29.91°+10.3°) -42

  SH = 73·0.84547 -42 = 19.720 . . . . feet

The height of the statue is about 19.72 feet.

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