find the height of the building

Question

The angle of elevation to the top of a building in New York is found to be 15 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 your answer to four decimal places.)

Answer 1

Artavius,

You asked –

The angle of elevation to the top of a building in New York is found to be 15 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 your answer to four decimal places.)

Answer:

When doing trigonometry problems, it is important to draw diagrams to ensure proper understanding.  Here is a diagram of this situation.

   |*

   |       *

H |              *

   |                       *

   |_______15deg___*

              D = 1 mile

We know that the tangent (angle) = opposite side / adjacent side.  From the diagram, the angle is 15 degrees, the adjacent side is 1 mile long.  Tangent (15 deg) = H/1.  Solving for H we find that H = 1*tangent (15 deg). Using your calculator (make sure you set the computations to be made in degrees).

H= 1* 0.26794919243 = 0.2679 miles or 0.2679*5280 ft/mile = 1414.7717 feet.

Regards,

Ray