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.
∠EMF=∠TMG
∠EFM=∠TGM=90∘
ΔMEF∼ΔMTG
1c.
¯TG:¯EF=¯GM:¯FM¯TG:60″=200″:80″¯TG⋅80″=60″⋅200″¯TG=60″⋅200″80″¯TG=150″
The tree is 150 inches tall.
2.
∠DBC=∠GBA (vertex angle)
∠DCB=∠GAB=90∘
ΔDBC∼ΔGBA
¯AG:¯CD=¯BA:¯BC¯AG:3′=15′:4′4′⋅¯AG=15′⋅3′¯AG=15′⋅3′4′
¯AG=1114′
The river is 1114 feet wide.
!