: A hot-air balloon is floating above a straight road. To estimate their height

Question

: 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 on two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 20 degrees and 15 degrees. How high is the balloon, in miles, rounded to two decimals? : 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 on two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 20 degrees and 15 degrees. How high is the balloon, in miles, rounded to two decimals?

Explanation / Answer

angle of depression is 20 deg and 15 deg

let first milepost distance = x

then 2nd milepost distance = x+1

angle of depression = 20 deg

tan 20 = h / x

tan 15 = h / (x+1)

.3639 = h/x

h = .3639x --------------- eqn 1

.2679 = h / (x+1)

.2679x + .2679 = h

.2679x + .2679 = .3639x

.2679 = .096x

x = 2.79 miles

h = .3639(2.79) = 1.015 miles

balloon is 1.015 miles high

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