The height of tree is 2.8 m
Given : TE = height of tree
MS = meter stick
XS = 3.5 m
ES = 6.5 m
Solution : In ΔXMS and ΔXTE
∠MXS=∠TXE (common angle) ---1
Reason : Correspoding angles are equal . since MS is parallel to TE so ∠XMS and ∠XTE will be corresponding angles
∠XSM =∠XET = 90° ---3
So, by 1 , 2 and 3 ΔXMS and ΔXTE are similar triangles by AAA property.
Since they are similar and we know that two triangles have their corresponding angles equal if and only if their corresponding sides are proportional.
Thus The height of tree is 2.8 m
(66cm statue) / (56cm shadow) = (height of tree, meters) / (27m shadow)
Multiply each side of the equation by (27m) :
height of tree = (66 cm) x (27m) / (56cm) = 31.82 meters or 31.8 meters
In addition to the angle of depression, we need either one of these:
-- the length of the tree's shadow on the ground
-- the slant distance direct from the tip of the shadow to the top of the tree.
I'm going out on a limb and guessing that on the page, next to that much of the
question, was a picture of the tree, with one of these additional items labeled.
There's an important reason why the publisher decided to go to the effort and
expense of printing the picture right there. I leave you to ponder the reason.
times bigger than the smaller one. So the height of the tree which is parallel to the metre stick is approx. 2.857 times bigger than the metre stick. So the height of the tree is 2.9 m (1 d.p).
TAN 49.3 = o/65
o = 65 * TAN 49.3
o = 75.56947167 feet