Math Question, Easy 10 Points?

Question

Two students want to determine the heights of 2 buildings.  They stand on the roof of the shorter building.  The students use a clinometer to measure the angle of elevation of the top of the taller building.  The angle of 44 degrees.  From the same position, the students measure the angle of depression of the base of the taller building.  The angle is 53 degrees.  The students then measure the horizontal distance between the two buildings.  The distance is 18.0m.  The students drew this diagram.  How tall is each building?

V. Singh · Accepted Answer

||&#92;A
   ||..&#92;
   ||....&#92;
   ||......&#92;
   ||...44.&#92; C
   ||.........|| 
   ||.........|| h1
   || 18 m ||
  -B-------D-

let height of the taller building is h and that of smaller is h1
   || A
   ||
   ||
   ||
   ||......... C
   ||.........|| 
   ||.........|| h1
   || 18 m ||
  -B-------D-
Consider the triangle CBD since angle of depression at C is 53 so angle CBD = 53 degrees
now since we know 
tan (angle CBD) = CD / BD
tan (53) = h1 / 18
or h1 (height of smaller building) = tan 53 * 18 = 23.8868 meter

...||&#92;A
...||..&#92;
h2||....&#92;
...||......&#92;
E ||...44.&#92; C
...||.18 m.|| 
...||.........|| 
...||.........||

Now just consider the upper triangle AEC. since angle of elevation at C is 44 so angle ECA = 44 degrees
now since we know 
tan (angle ACE) = AE / EC
tan (44) = h2 / 18
or h2 = tan 44 * 18 = 17.3824 meter

So total height of taller building h = h1 + h2
h = 17.3824  +  23.8868 = 41.2692 meter or 41.27 meter
and height of smaller building h1 = 23.8868 or 23. 89 meter

Hope this helped

Vick

W · Answer

Draw out your diagram, you should notice that you have two right angle triangles both with the length of one side being 18m.  The angle of one is 44 and the other is 53. 

Learn your trigonometry formulas.

SOH CAH TOA

Which stands for 

SOH : Sin = Opposite over hypotenuse

CAH : Cos = Adjacent over hypotenuse

TOA : TAN = Opposite over adjacent

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Math Question, Easy 10 Points?

2 Answers