partscoretotalsubmissions1--11/3An observer, whose eyes are 1.80 m above the ground, is standing 33.0 m away from a tree. The ground is level, and the tree is growing perpendicular to it. The observer's line of sight with the treetop makes an angle of 17.0° above the horizontal. How tall is the tree?
2007-09-06 07:24:30 · 1 answers · asked by Marianna E 1 in Science & Mathematics ➔ Physics
Draw a line parallel to the ground from teh observer's eyes to the tree. Let the height of the tree above that line be h. The observer looks up at an angle q a distances d from the tree so there is a right triangle formed by the line you drew, which is d long, the height of the tree above that line h, and the observer's line of sight. Since h is the side opposite q and d the side adjacent,
tan(q) = h/d but you know q and d so h = d tan(q)
using d = 33 and q =17 deg you get h = 10.1 m
But you measured from the height of the observer's eyes so you have to add in the 1.8 m. Thus the tree is:
tree height = 10.1+1.8 = 11.9 m
2007-09-06 07:37:27 · answer #1 · answered by nyphdinmd 7 · 1⤊ 0⤋