Posted by Anonymous on .
Pine Tree In order to estimate the height h of a tall pine tree, a student places a mirror on the ground and stands where she can see the top of the tree, as shown. The student is 6 feet tall and stands 3 feet from the mirror which is 11 feet from the base of the tree. What is the height h (in feet) of the pine tree?

geometry 
Reiny,
Can't see your diagram, but I know the question.
You have similar triangles, so use ratios
h/11= 6/3
h = 11(2) = 22 
geometry 
donmathuguina,
let x height of pine tree.
a=3 ,b=11, d=a+b, y=6 which is height of student. x=(dyay)/a ans.22
not all the time ratio is applicable.
alternate solution. you took the angle both triangle in terms of x, tangentx/d & tangentx/b. make an equation then substitute. ans still the same.