Kathy P. answered • 01/21/21
Mechanical Engineer with 10+ years of teaching and tutoring experience
Given: The angle of elevation to the top of a tall building is 10 degrees,
from the ground, from a distance of 0.9 miles.
Find: The height of the building.
SOLUTION:
Visualize or sketch a 10 degree angle, in the first quadrant.
Visualize or sketch a vertical line that puts the 10-degree-angle inside the triangle.
The horizontal base of the triangle is 0.9 miles.
The height of the triangle is the height of the building.
Tan(10) = [height] / [base]
Tan(10) = [height] / [0.9]
height = (0.9)*Tan(10)
height = 0.1587 miles.
Extra: Convert to feet
height = (0.1587 miles)*(5280 ft / mile)
height = 837.91 feet
