trigonometry help please?
here is the question, i have tried it a few times but i cant figure out the right answer, help please:
An observer, whose eyes are 1.77 m above the ground, is standing 27.0 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?
- RackbraneLv 71 decade agoBest Answer
AB be the tree (A at the top, B on the ground),
CD be the observer (C eye level, D ground),
CE be a horizontal line with E on the tree.
In triangle AEC, angle AEC = 90 deg, angle AEC = 17 deg.
EC = 27.0 m.
AE / EC = tan(AEC)
AE = EC tan(AEC)
= 27.0 tan(17).
The height of the tree is:
AB = AE + EB
= AE + CD
= 27.0 tan(17) + 1.77
= 10.0 m.