a girl 1 m tall is standing 6m away from the base of a lamp post . if the lamp is 4 m high then find the length of her shadow About the author Sophia
Answer: Step-by-step explanation: Using trigonometric ratios. Let AB be the height of lamp post. Now, in right △CDE, ⇒tanθ= DC ED = 4.8 1.6 = 3 1 ⟶(1) In , △ACB, ⇒tanθ= BC AB = 3.2+4.8 AB = 8 AB ⟶(2) From (1)&(2) we get ⇒ 3 1 = 8 AB ⇒AB= 3 8 =2.67m ∴ Height of the lamp post =2.67m (ii) Using similar triangles : In △CDE&△CBA i)∠CDE=∠CBA=90° ii)∠DCE=∠BCA (Common) ∴△CDE∼△CBA ( By AA similarities ) Hence, AB DE = BC CD ⇒AB= CD DE×BC = 4.8 1.6×8 = 3 8 =2.67m ∴ Height of lamp post =2.67m. Hence, the answer is 2.67. Reply
Answer:
Step-by-step explanation:
Using trigonometric ratios.
Let AB be the height of lamp post.
Now, in right △CDE,
⇒tanθ=
DC
ED
=
4.8
1.6
=
3
1
⟶(1)
In , △ACB,
⇒tanθ=
BC
AB
=
3.2+4.8
AB
=
8
AB
⟶(2)
From (1)&(2) we get
⇒
3
1
=
8
AB
⇒AB=
3
8
=2.67m
∴ Height of the lamp post =2.67m
(ii) Using similar triangles :
In △CDE&△CBA
i)∠CDE=∠CBA=90°
ii)∠DCE=∠BCA (Common)
∴△CDE∼△CBA ( By AA similarities )
Hence,
AB
DE
=
BC
CD
⇒AB=
CD
DE×BC
=
4.8
1.6×8
=
3
8
=2.67m
∴ Height of lamp post =2.67m.
Hence, the answer is 2.67.