Math, asked by Pallavarayar07, 1 year ago

As observed from the top of a light house, 100m above sea level, the angle of depression of a ship, sailing directly towards it, changes from 30 degree to 45 degree. Determine the distance traveled by the ship during the period of observation.

Answers

Answered by varsha36
2
30 + 45 =75
100 - 75 =25
Answered by silentlover45
10

\huge\underline\mathfrak{Diagram:-}

\underline\mathfrak{Given:-}

  • \: \: \: \: \: \: \: Height \: \: of \: \: of \: \: light \: \: house \: \: = \: \:  {100m}

  • \: \: \: \: \: \: \: Angle \: \: of \: \: depression \: \: of \: \: {1st} \: \: ship \: \: = \: \: {45}  \degree

  • \: \: \: \: \: \: \: Angle \: \: of \: \: depression \: \: of \: \: {2nd} \: \: ship \: \: = \: \: {30}  \degree

\underline\mathfrak{To \: \: Find:-}

  • \: \: \: \: \: Distance \: \: between \: \: two \: \: ship?

\underline\mathfrak{Solutions:-}

  • \: \: \: \: \: \: \: AB \: \: = \: \: {100m}

  • \: \: \: \: \: \angle ACB \: \: = \: \: {45} \degree

  • \: \: \: \: \: \angle ADB \: \: = \: \: {30} \degree

\: \: \: \: \: \therefore \: In \: \: \triangle \: ABC.

\: \: \: \: \: \leadsto \frac{100}{BC} \: \: = \: \: tan {45}  \degree

\: \: \: \: \: \leadsto {BC} \: \: = \: \: {100m}

\: \: \: \: \: \therefore \: In \: \: \triangle \: ABD.

\: \: \: \: \: \leadsto \frac{100}{BC \: + \: x} \: \: = \: \: tan {30}  \degree

\: \: \: \: \: \leadsto {100} \: \: = \: \: \frac{1}{\sqrt{3}} \: \times \: {({100} \: + \: x)}

\: \: \: \: \: \leadsto {{100}\sqrt{3}} \: \: = \: \: {100} \: + \: x

\: \: \: \: \: \leadsto {{100}\sqrt{3}} \: - \: {100} \: \: = \: \: x

\: \: \: \: \: \leadsto {100} \: {({\sqrt{3}} \: - \: {1})} \: \: = \: \: x

\: \: \: \: \: \leadsto {100} \: {({1.732} \: - \: {1})} \: \: = \: \: x

\: \: \: \: \: \leadsto {100} \: \times \: {0.732} \: \: = \: \: x

\: \: \: \: \: \leadsto {100} \: \times \: \frac{732}{1000} \: \: = \: \: x

\: \: \: \: \: \leadsto \frac{732}{10} \: \: = \: \: x

\: \: \: \: \: \leadsto {x} \: \: = \: \: {73.2m}

  • \: \: \: \: \: Hence, \: \: distance \: \: between \: \: two \: \: {73.2m}

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