Question
Two dogs are 180 ft apart on opposite sides of a tree. The angles of elevation from the dogs to the top of the tree are 35 degrees and 23 degrees.
What is the height of the tree?
What is the height of the tree?
Answers
drwls
Let X be the distance of the dog with the 35 degree elevation angle from the tree. The other dog is 180-X away (in feet). Let H be the height of the tree. You have these two equations in two unknowns:
H/X = tan 35 = 0.7002075
H/(180-X) = tan 23 = 0.4244748
Solve for X first by eliminating H.
(180-X)/X = tan35/tan23 = 1.64959
180 - X = 1.64959 X
X = 180/2.64959 = 67.935 feet
180-X = 112.065 ft
H = X tan 35 = 47.569 ft
H/X = tan 35 = 0.7002075
H/(180-X) = tan 23 = 0.4244748
Solve for X first by eliminating H.
(180-X)/X = tan35/tan23 = 1.64959
180 - X = 1.64959 X
X = 180/2.64959 = 67.935 feet
180-X = 112.065 ft
H = X tan 35 = 47.569 ft
May
Thanks!