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3.Trigonometrical Ratios, Functions and Identities
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Observe that, at any instant, the minute and hour hands of a clock make two angles between them whose sum is $360^{\circ}$. At $6: 15$ the difference between these two angles is $....^{\circ}$
A
$165$
B
$170$
C
$175$
D
$180$
(KVPY-2012)
Solution
(a)
At 6: 15,
the minutes hand makes an angle is $\alpha$.
$\therefore \quad \alpha =90^{\circ}+15 \times\left(\frac{1}{2}\right)^{\circ}$
$\alpha =\left(\frac{195}{2}\right)^{\circ}$
and hour hand is $\beta$.
Given, $\alpha+\beta=360^{\circ}$
$\therefore \quad \beta =360^{\circ}-\alpha$
$=360^{\circ}-\left(\frac{195}{2}\right)^{\circ}=\left(\frac{525}{2}\right)^{\circ}$
Difference between their angles
$=\frac{525}{2}-\frac{195}{2}=\frac{390}{2}=165^{\circ}$
Standard 11
Mathematics
