SarkariPYQ

SSC CGL 2022 PYQ — Question 64

SSC CGL - 21 April 2022 - Shift 3 • Quantitative Aptitude • Q64

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The length of the shadow of a vertical tower on level ground increases by 8.4 cm when the altitude of the sun changes from 45° to 30°. What is the height of the tower (in m)?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 4.2 ( 3+1\sqrt{3}+1)

When altitude of Sun is 45°, shadow length = h / tan 45 = h

When altitude of Sun is 30°, shadow length = h / tan 30 = h√3

Increase in shadow length = h√3 – h = h(√3 – 1).

According to question,

h(√3 – 1) = 8.4 cm

So, h = 8.4 / (√3 – 1)

Multiply numerator and denominator by (√3 + 1):

h = 8.4(√3 + 1) / (3 – 1)

h = 4.2(√3 + 1)