Using Trigonometry to Find the
Height of a Building
To estimate the
height, H, of a building, measure the distance, D, from the point
of observation to the base of the building and the angle, q (theta),
shown in the diagram. The ratio of the height H to the distance
D is equal to the trigonometric function tangent q (H/D = tan
q). To calculate H, multiply tangent q by the distance D (H =
D tan q). The angle can be roughly estimated by pointing one
arm at the base of the building and the other arm at the roof
and judging whether the angle formed is close to 15°, 30°,
45°, 60°, or 75°. The angle can be estimated more
accurately with a protractor and a plumb bob made of a pencil
hanging from a string. Hang the plumb bob from the zero point
in the middle of the straight edge of the protractor. Sight along
the edge of the protractor at the roof of the building. Measure
the angle formed by the straight edge of the protractor and the
plumb bob. Subtract this angle from 90°.
- The earliest applications
of trigonometry were in the fields of navigation, surveying,
and astronomy, in which the main problem generally was to determine
an inaccessible distance, such as the distance between the earth
and the moon, or of a distance that could not be measured directly,
such as the distance across a large lake. Other applications
of trigonometry are found in physics, chemistry, and almost all
branches of engineering, particularly in the study of periodic
phenomena, such as vibration studies of sound, a bridge, or a
building, or the flow of alternating current.
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