Ramesh places a mirror on level ground to determine the height of the pole (with traffic light fired on it) .He stands at a certain distance so that he can see the top of the pole reflected from the mirror. Ramesh's eye level 1.5m above from the ground. The distance between Ramesh and the pole is 1.8m and 6m respectively.
Answers
The height of the tree is 3 m.
Step-by-step explanation:
Referring to the figure attached below, we have,
BC = the distance between the tree and the mirror = 2.5 m
CD = the distance of Anjali from the mirror = 1.5 m
ED = Anjali’s eye level from the ground = 1.8 m
AB = the height of the tree
Now, consider ΔCDE and ΔCBA, we have
∠C = ∠C ...... [common angle]
∠ABC = ∠EDC = 90° ..... [since both the man and the tower stands vertical with the ground]
∴ By AA similarity, ΔCDE ~ ΔCBA
We know the corresponding sides of the similar triangles are proportional to each other.
∴ CD / BC = ED / AB
⇒ 1.5 / 2.5 = 1.8 / AB
⇒ AB = [1.8 x 2.5] / 1.5
⇒ AB = 3 m ← height of the tree
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Given : Ramesh’s eye level is 1.5 m above the ground. The distance of Ramesh and the pole from the mirror are 1.8 m and 6 m respectively.
To Find : (i) Which criterion of similarity is applicable to similar triangles?
(a) SSA
(b) ASA
(c) SSS
(d) AA
(ii) What is the height of the pole?
(a) 6 metres
(b) 8 metres
(c) 5 metres
(d) 4 metres
(iii) If angle of incidence is i , which of the following is correct relation?
(a) tan i=5/6
(b) tan i= 6/5
(c) tan i= 3/5
(d) tan i= 5/3
Solution:
criterion of similarity is applicable to similar triangles AA
as common angle and right angles are common
height of the pole = h
=> h/1.5 = 6/1.8
=> h = 9/1.8
=> h = 5 m
height of the pole = 5 m
Tan i = 5/6
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