Height of an object given angles of depression

In summary, the problem involves a hot-air balloon floating above a straight road. The balloonists measure the angles of depression to two consecutive mileposts on the road to estimate the balloon's height. Using trigonometric functions and the Pythagorean theorem, it is possible to calculate the height of the balloon by constructing right triangles. There is enough given information to find a numerical value for the balloon's height.
  • #1
DJ24
21
0

Homework Statement



A hot-air balloon is floating above a straight road. To estimate their height above the ground, the balloonists simultaneously measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 20o and 22o. How high is the balloon?


Homework Equations




  • the trigonometric functions

  • the Pythagorean theorem

The Attempt at a Solution



I have just tried constructing different right triangles, but always end up not having enough information to calculate side lengths and angles.
 
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  • #2
From the balloon draw two angles of depression which meet ground at P and Q. Let OB be the height of the balloon from the ground. In the problem it is given that PQ = 1 mile. Let OP be x. Now you have two right triangles, OPB and OQB.
 
  • #3
Is there enough given information to find a numerical value for OB?
 
  • #4
There is enough information. The attachment should help once it's approved
 

Attachments

  • balloon.bmp
    45.5 KB · Views: 1,211

Related to Height of an object given angles of depression

What is the "height of an object given angles of depression"?

The "height of an object given angles of depression" refers to a mathematical method used to determine the height of an object based on the angles formed by the observer's line of sight and the object's base.

How is the height of an object calculated using angles of depression?

The height of an object can be calculated using the tangent function, where the tangent of the angle of depression is equal to the object's height divided by the distance from the observer to the object. This can be represented as h = d * tan(theta), where h is the height, d is the distance, and theta is the angle of depression.

What information is needed to calculate the height of an object using angles of depression?

To calculate the height of an object, you will need to know the angle of depression and the distance from the observer to the object. This can be measured using a protractor and a measuring device, such as a ruler or a measuring tape.

What are the common applications of calculating the height of an object using angles of depression?

This method is commonly used in fields such as surveying, engineering, and architecture to determine the height of buildings, towers, or other structures. It can also be used in navigation, such as determining the height of land features or objects from a ship at sea.

What are the potential sources of error when calculating the height of an object using angles of depression?

The accuracy of the calculated height can be affected by errors in measuring the angle of depression or the distance to the object. Other factors such as atmospheric conditions and human error can also contribute to inaccuracies in the calculation.

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