a man sees the top of a tower in a mirror which is a distance of 80.4m from the tower the mirror is on the ground facing upwards the man is 0.6m away from the mirror and his height is 1.8m how tall is the tower
Answers
The tower is 241.2 m tall.
Step-by-step explanation:
Referring to the figure attached below, we have,
BC = the distance between the man and the mirror = 80.4m
CD = the distance of the man from the mirror = 0.6 m
ED = the height of the man = 1.8 m
AB = the height of the tower
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
⇒ 0.6 / 80.4 = 1.8 / AB
⇒ AB = [1.8 x 80.4] / 0.6
⇒ AB = 241.2 m ← the height of the tower
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