Question

1.
A tower of height 30 metres casts a shadow of length 40 meters at a certain instant. When the sun's
elevation increases by Tan -- the length of the shadow cast by the tower, in meters is
1) 20
2) 25
3) 30
4 45​

Answer 1

The shadow cast by the tower is 30 meters

Option 3 is correct

Step-by-step explanation:

Please refer attachment for figure.

A tower of height 30 meters casts a shadow of length 40 meters at a certain instant.

In ΔABC, ∠B = 90°

$\tan\angle C=\dfrac{AB}{BC}$

$\tan\angle C=\dfrac{30}{x}$

In ΔABD, ∠B = 90°

$\tan\angle D=\dfrac{AB}{BD}$

$\tan\angle D=\dfrac{30}{40}$

When the sun's  elevation increases by $\tan^{-1}\dfrac{1}{7}$

Therefore, $\angle C-\angle D=\tan^{-1}\dfrac{1}{7}$

Apply tan both sides

$\tan(\angle C-\angle D)=\tan(\tan^{-1}\dfrac{1}{7})$

$\dfrac{\tan\angle C-\tan\angle D}{1+\tan\angle C\cdot \tan\angle D}=\dfrac{1}{7}$

$\dfrac{\dfrac{30}{x}-\dfrac{30}{40}}{1+\dfrac{30}{x}\cdot\dfrac{30}{40}}=\dfrac{1}{7}$

$\dfrac{1200-30x}{40x+900}=\dfrac{1}{7}$

$8400-210x=40x+900$

$250x=7500$

$x=\dfrac{7500}{250}$

$x=30$

Hence, the shadow cast by the tower is 30 meters

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Height and distance

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Answer 2

Answer:

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