Height of an object given angles of depression

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Homework Help Overview

The problem involves determining the height of a hot-air balloon using angles of depression measured to two consecutive mileposts on the ground. The angles of depression are given as 20 degrees and 22 degrees.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss constructing right triangles based on the angles of depression and the distance between the mileposts. There are attempts to relate the height of the balloon to the geometry of the situation, but concerns about insufficient information are raised.

Discussion Status

Some participants are exploring the geometric relationships involved, while others question whether the provided information is adequate for a numerical solution. An attachment is mentioned that may provide additional insights once approved.

Contextual Notes

There is a mention of the distance between the mileposts being 1 mile, but the implications of this distance in relation to the angles of depression are still under discussion.

DJ24
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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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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.
 
Is there enough given information to find a numerical value for OB?
 
There is enough information. The attachment should help once it's approved
 

Attachments

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