Mathematics

Question

from a distance 42 feet from the base of the building the angle of elevation of the top of the building a 67 degrees estimate the height of the building to the nearest Foot
A.18ft
B.16ft
C.39ft
D.99ft

2 Answer

  • tanα=h/d

    h=dtanα, we are told that d=42ft and α=67° so

    h=42tan67 ft

    h≈99 ft (to nearest foot)
  • Answer:

    D. 99 ft.  

    Step-by-step explanation:

    Let h be the height of building.

    We have been given that from a distance 42 feet from the base of the building the angle of elevation of the top of the building a 67 degrees.

    We can see from our attachment that the building and distance between the base of building and angle of elevation forms a right triangle. The side with length 42 ft is adjacent side and height of building is opposite side of our right triangle.

    Since we know that tangent relates the opposite side of right triangle with the adjacent side.

    [tex]\text{Tan}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]

    Upon substituting our given values in above formula we will get,

    [tex]\text{tan}(67^o)=\frac{h}{42}[/tex]

    [tex]2.355852365824=\frac{h}{42}[/tex]

    [tex]2.355852365824\times 42=\frac{h}{42}\times 42[/tex]

    [tex]98.945799364608=h[/tex]

    [tex]h\approx 99[/tex]

    Therefore, the height of the building is 99 ft and option D is the correct choice.

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