A tower of height $30$ meters casts a shadow of length $40$ meters at a certain instant. When the sun's elevation increases by ${tan}^{- 1} \frac{1}{7}$ , the length of the shadow cast by the tower, in meters is

20

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25

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30

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45

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Solution

The correct option is C $30$
$t a n θ = \frac{30}{d}$
$(\frac{t a n θ + t a n α}{1 - t a n θ t a n α}) = \frac{30}{d}$
$\frac{\frac{1}{7} + \frac{3}{4}}{1 - \frac{3}{28}}$ $= \frac{30}{d}$
$d = 30$

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A tower of height 30 meters casts a shadow of length 40 meters at a certain instant. When the sun's elevation increases by tan−117, the length of the shadow cast by the tower, in meters is

The correct option is C 30tanθ=30d(tanθ+tanα1−tanθtanα)=30d17+341−328=30dd=30

A tower of height $30$ meters casts a shadow of length $40$ meters at a certain instant. When the sun's elevation increases by ${tan}^{- 1} \frac{1}{7}$ , the length of the shadow cast by the tower, in meters is

The correct option is C $30$
$t a n θ = \frac{30}{d}$
$(\frac{t a n θ + t a n α}{1 - t a n θ t a n α}) = \frac{30}{d}$
$\frac{\frac{1}{7} + \frac{3}{4}}{1 - \frac{3}{28}}$ $= \frac{30}{d}$
$d = 30$