PreCalc
posted by John .
A hotair 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 24° and 27°. How high is the balloon? (Round your answer to one decimal place.)

We form 2 rt triangles with a common ver. side.
tan27 = h/x.
Eq1: h = X*tan27 = 0.5095X.
tan24 = h/(X+1).
h = tan24*(x+1).
h = 0.4452(x+1).
h = 0.4452x + 0.4452.
0.5095x = 0.4452x + 0.4452.
0.5095x  0.4452x = 0.4452.
0.0643x = 0.4452.
X = 0.4452 / 0.0643 = 6.92. Miles.
h = x*tan27 = 6.92*tan27 = 3.5 Miles.
Respond to this Question
Similar Questions

Physics
A hot air balloon is ascending straight up at a constnat speed of 7.0 m/s. When th balloon is 12.0 m above the ground, a gun fires a pellet straight up from ground elvel with an initial speed of 30,0 m/s. Along the paths of the balloon … 
math
a hotair balloon is seen in the sky simultaneously by two observers standing a t two different points on the ground. (the 2 people are facing each other and the balloon is in between them in the air.)they are 1.75 miles apart on level … 
math
a hotair balloon is seen in the sky simultaneously by two observers standing a t two different points on the ground. (the 2 people are facing each other and the balloon is in between them in the air.)they are 1.75 miles apart on level … 
Hotair balloon
A hotair balloon is 180 ft above the ground when a motorcycle passes directly beneath it (travelling in a straight line on a horizontal road) going at a constant speed of 60 ft/s. If the balloon is rising vertically at a rate of 15 … 
physics
A hotair balloon plus cargo has a mass of 1740 {\rm kg} and a volume of 12030 {\rm m^3}. The balloon is floating at a constant height of 6.25 {\rm m} above the ground. What is the density of the hot air in the balloon? 
physics
A hotair balloon plus cargo has a mass of 1740 {\rm kg} and a volume of 12030 {\rm m^3}. The balloon is floating at a constant height of 6.25 {\rm m} above the ground. What is the density of the hot air in the balloon? 
AlgebraTrig Please Help ASAP
A balloon isin the vertical plane of two consecutive milestones of a road. The angles of depression of the stones as viewed from the balloon are 15 degrees and 17 degrees. Find the height of the balloon if (a) the stones are on opposite … 
physics
A hot air balloon is ascending straight up at a constant speed of 6.50 m/s. When the balloon is 13.0 m above the ground, a gun fires a pellet straight up from ground level with an initial speed of 34.0 m/s. Along the paths of the balloon … 
Trigonometry
A HOT AIR BALLOON IS 70 m ABOVE THE SEA. TWO BUOYS A AND B ARE DUE EAST OF THE BALLOON. THE ANGLE OF DEPRESSION FROM THE BALLOON TO BUOY A IS 60°. THE ANGLE OF DEPRESSION FROM THE BALLOON TO THE BUOY B IS 40°. CALCULATE DISTANCE … 
math
The angles of elevation of a balloon directly above a straight road, from two points of the ground on opposite sides of the balloon, are 78¡ã15' and 59¡ã47'. If the points are 5000ft apart, what is the height of the balloon?