SOLUTION: The angle of elevation from a point on the ground to the top of a tree is 35.3 degrees. The angle of elevation from a point 20 ft farther back to the top of the tree is 23.3 degree
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-> SOLUTION: The angle of elevation from a point on the ground to the top of a tree is 35.3 degrees. The angle of elevation from a point 20 ft farther back to the top of the tree is 23.3 degree
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Question 1129201: The angle of elevation from a point on the ground to the top of a tree is 35.3 degrees. The angle of elevation from a point 20 ft farther back to the top of the tree is 23.3 degrees. Find the height of the tree to 2 decimal places. Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! The angle of elevation from a point on the ground to the top of a tree is 35.3 degrees.
The angle of elevation from a point 20 ft farther back to the top of the tree is 23.3 degrees.
Find the height of the tree to 2 decimal places.
:
The tree top, bottom and points on the ground form right triangles
let t = the height of the tree
let d = distance from the point on the ground when the angle is 35.3 degrees
then
(d+20) = distance from the further point on the ground when the angle is 23.3 degrees
:
Use the tangent of the angles h = side opposite
Two position equations
tan(23.3) =
h = tan(23.3)*(d+20)
h = .43067d + 8.613
and
tan(35.3) =
h = tan(35.3) * d
h = .708d
h = h solve for d
.708d = .43067d + 8.613
.708d -.43067d = 8.613
.277d = 8.613
d =
d = 31.10 ft
Find h
h = .708(31.1)
h = 22.02 ft is the height of the tree
:
:
Check this using the other position which is 51.1 ft from the tree
tan(23.3) * 51.1 = 22.01 ft, close enough?
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