Another one

Nov 2015
17
0
Baltimore
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 are found to be 16o and 12o. How high is the balloon?
 

pickslides

MHF Helper
Sep 2008
5,237
1,625
Melbourne
How far apart are the mileposts apart?
 
Feb 2015
2,255
510
Ottawa Ontario
Not in Australia!!
Hi Picks :)
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
The original post said "two consecutive mile posts". So, drawing the line from the balloon perpendicular to the road, we have two right triangles, one with angle 90- 16= 74 degrees, "near leg" of length h miles and "opposite leg" of length x miles. tan(74)= x/h. The second right triangle has angle 90- 12= 78 degrees, "near leg" of length h miles and "opposite leg" of length 1- x miles. tan(78)= (1- x)/h. You have two equations in x and h.