SOLUTION: two points on the same side of a tree are 19.8 meters apart.the angles of elevation of the top of the tree are 21 degrees and 16 degrees from the other point find the height of the

Algebra ->  Trigonometry-basics -> SOLUTION: two points on the same side of a tree are 19.8 meters apart.the angles of elevation of the top of the tree are 21 degrees and 16 degrees from the other point find the height of the      Log On


   

Question 1110493: two points on the same side of a tree are 19.8 meters apart.the angles of elevation of the top of the tree are 21 degrees and 16 degrees from the other point find the height of the tree
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
let h be the height of the tree and x be the distance from the tree to the first point(21 degrees elevation), then
:
tan(21) = h/x
tan(16) = h/(x+19.8)
:
we have two equations in 2 unknowns
:
1) h = tan(21) * x = 0.3839x
2) h = tan(16) * (x+19.8) = 0.2867 * (x+19.8) = 0.2867x +5.6767
:
set equation 1 = equation 2
:
0.3839x = 0.2867x +5.6767
:
0.0972x = 5.6767
:
x = 58.4023
:
use equation 1
:
h = 0.3839 * 58.4023 = 22.4206 approximately 22.4
:
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height of tree is 22.4 meters
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