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# The height TR of a tree may be measured by using .

## Tags: Mathematik     RASTA 15:03 Uhr, 04.01.2022

Tag, need help in starting this problem.
Vielen Dank im Voraus.

The height TR (there is $a\phantom{\rule{0.12em}{0ex}}\overline{}$ on top $o\phantom{\rule{0.12em}{0ex}}$ the TR) of a tree may be measured by using similar triangles. A mirror is placed at point $M\phantom{\rule{0.12em}{0ex}}$ so that the top of the tree is sighted in the mirror by a person standing at point P. The person's eye is at point E. Given the measurements shown in the diagram , what is the length of TR?

I am attaching the pic

Für alle, die mir helfen möchten (automatisch von OnlineMathe generiert):
"Ich möchte die Lösung in Zusammenarbeit mit anderen erstellen."  supporter 15:19 Uhr, 04.01.2022

We can use the ray theorem = theorem of intersecting lines

$\frac{4+0,6}{0,6}=\frac{x\phantom{\rule{0.12em}{0ex}}}{1,8}$

$x\phantom{\rule{0.12em}{0ex}}=..$.  RASTA 17:35 Uhr, 04.01.2022

thank you. I will study that and post my work so you can rectifiy it.  RASTA 18:17 Uhr, 04.01.2022

when $i\phantom{\rule{0.12em}{0ex}}$ solve for $x\phantom{\rule{0.12em}{0ex}}$
$=4,9$ which is not listed among the possible answers.
Do I have to do sometihng elese?
can you send me a link to a tutorial bout this theorem becasue I have search online and have not found anything.  RASTA 18:15 Uhr, 06.01.2022

Hello, hope you're doing fine. can you send me a link to that theorem you say?
I don't seem to find it. thank you in advance What supporter possibly meant was the Intercept Theorem
see here: en.wikipedia.org/wiki/Intercept_theorem

But supporter applied it incorrectly, which then led to a wrong result in your calculation.
By the way, you also made a mistake when reshaping supporter's wrong approach by multiplying by $0.6$ instead of dividing.

You may also think of similar triangles. The triangles MRT and MPE are similar to each other, because they coincide at one angle (the right angle) and another angle (at $M\phantom{\rule{0.12em}{0ex}},$ law of reflection). Therefore, the ratio of corresponding sides is the same.

For further questions, show your attempts here.  RASTA 18:48 Uhr, 06.01.2022

okay, will do. thanks  RASTA 14:54 Uhr, 08.01.2022

In this problem triangle TRM is similar to EPM.

Using laws of similar triangles:

TR/EP = RM/PM .......proportional sides

TR = RM/ PM $\cdot$ EP $=\frac{4}{0,6}\cdot 1.8=12m\phantom{\rule{0.12em}{0ex}}$

thanks for the help Correct, the height is $12m\phantom{\rule{0.12em}{0ex}}$  RASTA 16:26 Uhr, 08.01.2022

thanks a lot.