Thread: How many meters is the balloon from the starting point on the ground?

Twenty minutes after being launched, a hot-air balloon has risen to an altitude of 300m. The pilot can still see the starting point at a 25 degree angle of depression. How many meters is the balloon from the starting point on the ground?
Please show work.

300 meters.... trick question?

tan = opp/adj
tan(25) =300/x
x=643.35m
total distance =sqrt(x^2 +(300)^2)
total distance ~710m

the hot air balloon risen to the altitude of 300 m so that means that it is 300 meters from the ground not on the starting point

the angle of depression is 25degrees

because it is an angle of depression the altitude to the ground is opposite to the angle and because we are finding for the distance of the hot air balloon to the starting point so we are finding for the hypotenuse.

we already know the opposite side of the angle and the angle itself. we are finding for the hypotenuse so the function sine will be used

sine 25=300/h (h=hypotenuse)
h=300/sine 25
h=709.86

so the balloon is 709.86m away from the starting point


hope this helps.....