A meteorologist is using a theodolite (an angle-measuring device) on a 1-meter tripod to find the height of a
weather balloon. She views the balloon through the theodolite at a 44° angle of elevation. A radio signal from the
balloon tells her that it is 1400 meters from the theodolite. How high is the balloon?
Answers
Given : A meteorologist is using a theodolite (an angle-measuring device) on a 1-meter tripod to find the height of a weather balloon. She views the balloon through the theodolite at a 44° angle of elevation. A radio signal from the balloon tells her that it is 1400 meters from the theodolite.
To find : How high is the balloon?
Solution:
Angle of Elevation = 44°
A radio signal from the balloon tells her that it is 1400 meters from the theodolite.
theodolite length = 1 m
Hence Distance of Baloon from person = 1400 + 1 = 1401 m
Sin ( Angle of elevation) = height of Balloon/Distance of Balloon
=> Sin 44° = height of Balloon/1401
=> height of Balloon = 1401 * Sin44°
=> height of Baloon = 973.2 m
Balloon is 973.2 m high
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