Answer
the distance between the posts is 1 mile
let x be the horizontal distance between the pole 1 and the ballon
Step-by-step explanation:
height of balloon = h
tan 24 = h/x
h = x tan 24
similarly
h= (x+1) tan 20
xtan 24 = (x+1) tan 20
Answer: approximately 399 feet
The more accurate value is 399.050828368008 feet, but this value is still approximate.
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Work Shown:
Refer to the diagram below.
To find x, we'll use the sine rule
sin(angle) = opposite/hypotenuse
sin(28) = x/850
850*sin(28) = x
x = 850*sin(28)
x = 399.050828368008 ...... make sure your calc is in degree mode
x = 399
I'm rounding to the nearest whole number since the given values (28 and 850) are also whole numbers. If your teacher provides other rounding instructions, then be sure to follow that.
The hot air balloon is approximately 399 feet off the ground.
