Question

a woman 1.65. tall stood 50m away from the foot of a tower,and observe that the angle of elevation of the top of the tower to be 50⁰ what is the height of the tower​

Answer 1

61.24 m to the nearest hundredth.

Explanation:

tan 50 = H / 50

H = 50 tan 50

Height of the tower = H + height of the woman

= 50 tan 50 + 1.65

= 61.2377 m

Answer 2

`\sf\huge\underline{\star Solution:-}`

`\rightarrow`Let the women's height be AE and distance between the women and tower be AC.

Also let the height of tower be BC.

`\rightarrow`Now, clearly it is forming a triangle.

So, in triangle ABC,

`\rightarrow`
`\sf{Tan50° \:= \: (BC)/(AC)}`

`\rightarrow`
`\sf{1.19 \:= \: (BC)/(50)}`

`\rightarrow`
`\sf{1.19 ×50\:= \: BC}`

`\rightarrow`
`\sf{59.5m\:= \: BC}`

`\rightarrow`Hence, BC = 59.5m

So, BD(total height of the tower)
`\sf{ = \:BC+CD}`

`\sf{= \:59.5+1.65}`

`\sf{=\: 61.15m}`

Therefore, total height of the tower =
`\sf\purple{ 61.15m.}`

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Hope it helps you:)