Question

THE SHADOW OF A TOWER AT A TIME IS THREE TIMES AS LONG AS ITS SHADOW WHEN ANGLE OF ELEVATION OF SUN IS 60*. FIND ANGLE OF ELEVATION AT THE TIME OF LONGER SHADOW.

Answer 1

Hope it will help u ........☺

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Answer 2

Answer:

30°

Step-by-step explanation:

Hi,

Let CD be the tower,

Let BC be the shadow, when angle of inclination is 60°,

Let Ф be the angle of inclination, when shadow is

3 times BC, and Let AC be its shadow at inclination Ф,

Consider Δ BCD, we have ∠DBC = 60°,

tan ∠DBC = CD/BC

CD = BC√3

Consider ΔACD,

∠DAC = Ф,

tan Ф = CD/AC

Given that AC = 3BC(3 times the shadow)

So, tan Ф = CD/3BC

But, CD = BC√3, so

tan Ф =  BC√3/3BC

= 1/√3

So, Ф = 30°.

Hence, the angle of elevation at the time of

longer shadow is 30°.

Hope, it helps !