Question 1110493
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
:
********************************
height of tree is 22.4 meters
********************************
: