Trigonometry: A 12.4 m flagpole is placed on top of a tall building
A 12.4 m flagpole is placed on top of a tall building. An observer, standing directly in front of the
building and flagpole, measures the angle of elevation to the bottom of the flagpole to be 42.5
◦
and to the top of the flagpole to be 48.2
◦
. Determine the height of the building, to the nearest
meter.
Solution:
Represent the given information on a diagram. Let the height of the building be h and the distance out from the building to the observer be d.
In 4BCD, h d = tan 42.5 ◦ and in 4ACD, h+12.4 d = tan 48.2 ◦ . Rearranging, h = d(tan 42.5 ◦ ) and h + 12.4 = d(tan 48.2 ◦ ). Substitute for h in the second equation,
d(tan 42.5 ◦ ) + 12.4 = d(tan 48.2 ◦ )
12.4 = d(tan 48.2 ◦ ) − d(tan 42.5 ◦ )
12.4 = d(tan 48.2 ◦ − tan 42.5 ◦ )
12.4 ÷ (tan 48.2 ◦ − tan 42.5 ◦ ) = d
61.35 ˙= d
But h = d(tan 42.5 ◦ ) ˙= 56.2
Solution:
Represent the given information on a diagram. Let the height of the building be h and the distance out from the building to the observer be d.
In 4BCD, h d = tan 42.5 ◦ and in 4ACD, h+12.4 d = tan 48.2 ◦ . Rearranging, h = d(tan 42.5 ◦ ) and h + 12.4 = d(tan 48.2 ◦ ). Substitute for h in the second equation,
d(tan 42.5 ◦ ) + 12.4 = d(tan 48.2 ◦ )
12.4 = d(tan 48.2 ◦ ) − d(tan 42.5 ◦ )
12.4 = d(tan 48.2 ◦ − tan 42.5 ◦ )
12.4 ÷ (tan 48.2 ◦ − tan 42.5 ◦ ) = d
61.35 ˙= d
But h = d(tan 42.5 ◦ ) ˙= 56.2
Therefore the height of the building is 56 m.
