Height of an object given angles of depression

[DJ24]

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 20^o and 22^o. 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.

 

[rl.bhat]

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.

 

[DJ24]

Is there enough given information to find a numerical value for OB?

 

[Bohrok]

There is enough information. The attachment should help once it's approved