1: Use this example to demonstrate: Points M and G are labeled and represent the Mirror and the point where the tree touches the ground.
a: Label points: T at the top of the tree, E at the person’s eye level, and F at the person’s feet
b: Explain how you can create two similar triangles using the AA similarity postulate. You can sketch the triangles separately if you would like (hint: if the person and tree stand up straight, they form 90-degree angles at the ground):
c: If EF = 60 inches, FM = 80 inches, and MG = 200 inches, how tall is the tree?
Hello buyya!
1b.
In optics, angles of incidence are equal to angles of reflection in the case of reflection.
\(\angle EMF=\angle TMG\)
\(\angle EFM=\angle TGM=90^{\circ}\)
\(ΔMEF\sim ΔMTG\)
1c.
\(\overline{TG}:\overline{EF}=\overline{GM}:\overline{FM}\\ \overline{TG}:60''=200'':80''\\ \overline{TG}\cdot 80''=60''\cdot 200''\\ \overline{TG}= \dfrac{60''\cdot 200''}{80''}\\ \overline{TG}=150''\)
\(The\ tree\ is\ 150\ inches\ tall. \)
2.
\(\angle DBC=\angle GBA\ (vertex\ angle )\)
\(\angle DCB=\angle GAB=90^{\circ}\)
\(ΔDBC\sim ΔGBA\)
\(\overline{AG}:\overline{CD}=\overline{BA}:\overline{BC}\\ \overline{AG}:3'=15':4'\\ 4'\cdot \overline{AG}=15'\cdot 3'\\ \overline{AG}=\dfrac{15'\cdot 3'}{4'}\)
\(\overline{AG}=11\frac{1}{4}'\)
\(The\ river\ is\ 11\frac{1}{4}\ feet\ wide. \)
!
