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The angle of elevation to the top of a Building in New York is found to be 8 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building. Round to the tenths. Hint: 1 mile = 5280 feet

Your answer is ? feet.

Respuesta :

mhanifa

Answer:

  • 742.1 ft

Step-by-step explanation:

The three points, the top and bottom of the building and the remote point form a right triangle where vertical and horizontal distances are the legs of this triangle.

Let the height be h.

Find its value using trigonometry:

  • tan 8° = h / 5280 ft
  • h = 5280 tan 8°
  • h = 742.1 ft (rounded)
semsee45

Answer:

742.1 ft  (nearest tenth)

Step-by-step explanation:

Angle of Elevation

If a person stands at a point and looks up at an object, the angle between their horizontal line of sight and the object is called the angle of elevation.

To find the height of the building, model as a right triangle and solve using the tan trigonometric ratio.

Tan trigonometric ratio

[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]

where:

  • [tex]\theta[/tex] is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle

Given information:

  • [tex]\theta[/tex] = Angle of elevation = 8°
  • A = Distance from base of building = 1 mile = 5280 feet
  • O = height of building

Substitute the given values into the formula and solve for height:

[tex]\implies \sf \tan(8^{\circ})=\dfrac{height}{5280}[/tex]

[tex]\implies \sf height=5280\tan(8^{\circ})[/tex]

[tex]\implies \sf height=742.1\:ft\:\:(nearest\:tenth)[/tex]

Learn more about angles of elevation here:

https://brainly.com/question/27933160

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