.Teacher gives an activity to the students to measure the height of the tree
and asks them who will do this activity. Anjali accepts the challenge she
places a mirror on level ground to determine the height of a tree. She
stands at a certain distance so that she can see the top of the tree reflected
from the mirror. Anjali’s eye level is 1.8m above ground, the distance of
Anjali and the tree from the mirror are 1.5m and 2.5m respectively. Answer
the question below.
Answers
Answer:
The distance of Anjali and the tree from the mirror is 1.5 m. The distance of the tree from the mirror is 2.5 m . ∴ h = 3 m. Therefore the height of the tree is 3m.
Question :
Teacher gives an activity to the students to measure the height of the tree and asks them who will do this activity. Anjali accepts the challenge. She places a mirror on level ground to determine the height of a tree. She stands at a certain distance so that she can see the top of the tree reflected from the mirror. Anjali’s eye level is 1.8m above ground, the distance of Anjali and the tree from the mirror are 1.5m and 2.5m respectively.
Answer the questions below :
i) Name the two similar triangles formed .
ii) State the criteria of similarity applicable here .
iii) Find the height of the tree
iv ) If ∆ ABM and ∆ CDM are similar, CD =6cm, MD = 8cm and BM =24cm then AB = ?
Answer :
i) ∆AMB ~ ∆CMD
ii) AA criterion
iii) 3m
iv ) 18cm
Solution :
i) ∆AMB ~ ∆CMD since ,
Angle ABM = Angle CDM (right angle)
and,
Angle AMB = Angle CMD ( Angle of incidence = Angle of reflection )
Therefore ∆AMB is similar to ∆CMD.
iI) AA Similarity since,
Angle ABM = Angle CDM (right angle)
and,
Angle AMB = Angle CMD ( Angle of incidence = Angle of reflection )
iii ) Height of tree = 3m because :
As ∆AMB ~ ∆CMD ,
AB/ CD = BM / MD
Hence , height of tree / 1.8 = 2.5 / 1.5
Therefore , height of trre = (1.8 × 2.5) ÷ 1.5
=3m
Hence, the height of tree is 3m
iv ) AB = 18cm because :
As ∆AMB ~ ∆CMD ,
AB/ CD = BM / MD
Therefore , AB / 6 = 24/8
AB = (24×6)/8
AB = 18
Therefore, AB = 18 cm
#SPJ3