Astatue 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.

  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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do your own work and don"t cheat.

step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.