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
Algebra.Com
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?
.
RELATED QUESTIONS
At a point on the ground 50 meters from the foot of a tree the measure of the angle of... (answered by mananth)
From a point A on level ground, the angle of elevation to the top of a tree is 38... (answered by josgarithmetic,MathTherapy)
From a point A on level ground, the angle of elevation to the top of a tree is 38... (answered by josgarithmetic,Edwin McCravy,math_tutor2020,MathTherapy)
The angle of elevation from the top of a tree to a point 30 feet from its base is 25... (answered by prince_abubu)
You are 90 ft from a tree. The angle of elevation from your eyes, which are 5 ft off the... (answered by josmiceli)
Due south of the base of a 100m tall lighthouse on level ground is a point A. The angle... (answered by ikleyn)
A backpacker notes that from a certain point on level ground, the angle of elevation to a (answered by Fombitz)
A surveying crew is tasked to measure the height of a mountain. From a point on level... (answered by xinxin)
Trina and Mazaheer are standing on the same side of a red maple tree. the angle of... (answered by solver91311)