SOLUTION: Please help me solve this problem:
There is a weather balloon going west between two stations that are 12 miles apart.
The balloon is angled from each station at 18 degrees and 7
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Question 612314: Please help me solve this problem:
There is a weather balloon going west between two stations that are 12 miles apart.
The balloon is angled from each station at 18 degrees and 76 degrees.
How high is the balloon?
*I need to a system of equations. I need to have two equations that are set equal to each other and I must use substitution. Then I must find the final answer of how high the balloon is.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
There is a weather balloon going west between two stations that are 12 miles apart.
The balloon is angled from each station at 18 degrees and 76 degrees.
How high is the balloon?
.
Apply trig:
Let h = height
and
x = length of base of 18 deg triangle
.
then
tan 18 = h/x (equation 1)
OR
tan 76 = h/(12-x) (equation 2)
.
Solve equation 1 for x:
tan 18 = h/x
xtan 18 = h
x = h/tan 18
.
plug above into equation 2 and solve for h:
tan 76 = h/(12-x)
tan 76 = h/(12-(h/tan 18))
dividing both sides by tan 18:
tan 76/tan 18 = h/(12tan 18-h)
(tan 76/tan 18)(12tan 18-h) = h
(tan 76/tan 18)(12tan 18) - (tan 76/tan 18)h = h
(tan 76/tan 18)(12tan 18) = h+(tan 76/tan 18)h
(tan 76/tan 18)(12tan 18) = h(1+(tan 76/tan 18))
(tan 76/tan 18)(12tan 18)/(1+(tan 76/tan 18)) = h
3.61 miles = h
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