Mirror
- Anjali places a mirror on level
ground to determine the height
of a tree (see the diagram). She
stands at a certain distance so
that she can see the top of the
tree reflected from the mirror. Tree
Ajnjali's eye level is 1.8 m above
the ground. The distance of
Anjali and the tree from the
mirror are 1.5 m and 2.5 m
respectively.
C Anjali's
(Eye-level)
1.8 m
2.5 m
1.5 m
(1)name two similar triangles that are formed
(2)state the criterion of similarity that is applicable
(3)find the height of the tree
Answers
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Consider the attached diagram while going through the following steps.
Given,
Ajnjali's eye level is 1.8 m above the ground.
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 .
Anjali's (Eye-level) is at 1.8 m from the ground level
Now consider,
In Δ ABC and Δ FDC,
∠ ACB = ∠ FCD (same angle)
∠ ABC = ∠ FDC = 90° (right angle)
using AA criteria, we have,
∴ Δ ABC ~ Δ FDC
⇒ FD / CD = AB / BC
⇒ h / 2.5 = 1.8 / 15
⇒ h = 2.5 × 1.8 / 15
∴ h = 3 m.
Therefore the height of the tree is 3m.
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Answer:
Given,
Anjali's eye level is 1.8 m above the ground.
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 .
Anjali's (Eye-level) is at 1.8 m from the ground level
Now consider,
In Δ ABC and Δ FDC,
∠ ACB = ∠ FCD (same angle)
∠ ABC = ∠ FDC = 90° (right angle)
using AA criteria, we have,
∴ Δ ABC ~ Δ FDC
⇒ FD / CD = AB / BC
⇒ h / 2.5 = 1.8 / 15
⇒ h = 2.5 × 1.8 / 15
∴ h = 3 m.
Therefore the height of the tree is 3m.
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