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Need help with this trigonometry word problem

The angle of elevation of the top of the building at a distance of 50 m from its foot on a horizontal plane is found to be 60°. Find the height of the building.
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1 Answer

5 votes

Answer:


\huge \boxed{ \boxed{ 50 √(3) \: or \: 86.6}}

Explanation:

to understand this

you need to know about:

  • trigonometry
  • PEMDAS

let's solve:

to find the height we need to use tan function because we are given adjacent and angle and we need to figure out opposite (height)
\tan(\theta)=(opposite)/(adjacent)

let opposite be AC

let adjacent be BC

according to the question:


\quad \: \tan( {60}^( \circ) ) = (AC)/(BC)

now we need a little bit algebra to figure out AC (height)


  1. \sf \: substitute \: the \: given\: value \: of \: BC : \\ \tan( {60}^( \circ) ) = (AC)/(50)

  2. \sf sustitute \: the \: value \: of \: \tan( {60}^( \circ) ) \: i.e \: √(3) : \\ √(3 ) = (AC )/(50)

  3. \sf cross \: multiplication: \\ 50 √(3) = AC

  4. \sf swap \: sides \: (your \: wil) : \\ AC = 50 √(3) \\AC = 86.6 \: ( \sf \: decimal \: if\: needed)


\text{we are done!}

Need help with this trigonometry word problem The angle of elevation of the top of-example-1
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