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frez [133]
3 years ago
15

The angle of elevation of the top of a tower from two points 121 m and 144 m away from the foot of the tower on th same side are

found to be complementary. find the height of the tower.​
Mathematics
1 answer:
Dennis_Churaev [7]3 years ago
6 0

Answer:

132 m

Step-by-step explanation:

Refer to attachment for figure.

In smaller triangle with angle theta , we have ,

⇒ tanθ = p/b

⇒ tanθ = h/121m

⇒ tanθ = h/121 m

<u>In</u><u> </u><u>triangle</u><u> </u><u>with</u><u> </u><u>angle </u><u>9</u><u>0</u><u>-</u><u>∅</u>

⇒ tan(90-θ) = p/b

⇒ cot θ = h/144 m

Multiplying these two ,

=> tanθ . cotθ = h/121 m × h/144m

=> 1 = h²/ (121 m × 144m )

=> h² = 121m × 144m

=> h= √ ( 121m × 144m)

=> h = 11m × 12m

=> h = 132 m

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