Mathematics, 22.06.2019 09:50 geekymuin

Find the height of the tree to the nearest tenth of a foot.

Answers: 3

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Answer from: ally6440

$\frac{height _{1} }{shadow_{1}} = \frac{height _{2} }{shadow_{2}}$

$\frac{height _{1} }{27m} = \frac{66cm}{56cm}$

$\frac{height _{1} }{2700cm} = \frac{66cm}{56cm}$

$2700*66=56*h _{1}$

$178200=56h _{1}$

$3182.1cm=h _{1}$

$\frac{3182.1cm}{1000cm} = 3.2m$

height:3.2m

Answer from: muziqbox594

Answer from: cman8228

Answer from: gin9

The height of tree is 2.8 m

Step-by-step explanation:

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

∠XMS=∠XTE ---2

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.

⇒ $\frac{XS}{XE} =\frac{MS}{TE}$

⇒ $\frac{3.5}{10} =\frac{1}{TE}$

⇒ $TE =\frac{1*10}{3.5}$

⇒ TE =2.8

Thus The height of tree is 2.8 m

Answer from: jbismyhusbandbae

As long as everything is on level ground with uniform elevation, and everything happens at the same time of day (with the sun at the same height in the sky) ...

(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

Answer from: floreschachi7506

No answer is possible using only the information given in the question.
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.

Answer from: breannaasmith1122

Ok, what you have there is two similar triangles (the sides have the same proportions in each). The bigger triangle is
(6.5+3.5)/3.5≈2.857
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).

Answer from: calebcoolbeans6691

TAN = Opposite / Adjacent
TAN 49.3 = o/65
o = 65 * TAN 49.3
o = 75.56947167 feet

Answer from: uchechukwueigwe

the height of the tree to the nearest tenth is 16.8 feet

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