Math, asked by riteshchauhan6085, 1 year ago

The horizontal distance between two poles is 15m .the angle of depression of the top of first pole as seen fdrom the top of second pole is 30 degree if the height of the second pole is 24 m, find the height of the first pole.

Answers

Answered by koushik3
3

24 - 5 \sqrt{3}
Answered by VelvetBlush
4

Let AB be the pole of height h metres and CD be the second pole of height 24m.

Draw CF||BD and AE ||BD.Then,

BD = AE = 15., CE = (24 - h) m

\sf\angle{{CAE}=\angle{ACF}=30°}

From right ∆AEC, we have

\longrightarrow\sf{tan\:30°= \frac{CE}{AE}=\frac{1}{ \sqrt{3} }  =  \frac{24 - h}{15}}

\longrightarrow\sf{\frac{15}{ \sqrt{3} }  = 24 - h}

\longrightarrow\sf{h = 24 -  \frac{15}{ \sqrt{3} }  = 24 - 5 \sqrt{3}}

\longrightarrow\sf{24-5×1.732}

\longrightarrow\sf{24-8.66}

\longrightarrow{\boxed{\sf{\red{15.34m}}}}

Hence, the height of the first pole = 15.34m.

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