Question

If the ratio of the angels produced by two unequal chords of a circle at the center of it is 5:2 and sexagesimal value of the second angle 30° then find the sexagesimal and circular value of the first angle.​

Answer 1

Sᴏʟᴜᴛɪᴏɴ :-

Let us Assume That, Angle produced by 2 unequal chords at centre = 5x & 2x .

Now, we have given That,

→ sexagesimal value of the second angle = 30°

So,

→ 2x = 30°

→ x = (30/2)

→ x = 15° .

Than,

→ 5x = first angle = 15 * 5 = 75° . (Ans.)

Now, we know That, 180° = π

Therefore,

→ 180° = π

→ 1° = (π/180)

→ 75° = (π/180) * 75 = (75π/180) = (5π/12) (Ans.)

Hence, The Sexagesimal measure of the first angle is 75° and Circular measure is (5π/12).

Answer 2

$\large\sf Answer :$

Let the Angles subtended be 5n and 2n.

⠀

$\underline{\bigstar\:\textsf{According to the Question :}}$

$:\implies\sf First\:Angle=\dfrac{Second\:Angle}{Second\:Angle\:Ratio} \times First\:Angle\:Ratio\\\\\\:\implies\sf First\:Angle = \dfrac{30}{2n} \times 5n\\\\\\:\implies\sf First\:Angle = 15 \times 5\\\\\\:\implies\underline{\boxed{\sf First\:Angle = 75^{\circ}}}$

$\therefore\:\underline{\textsf{Sexagesimal value of first angle is \textbf{75 ^{\circ} }}}.$

$\rule{200}{2}$

$\underline{\bigstar\:\textsf{Circular Value of First Angle :}}$

$\dashrightarrow\sf\:\:180^{\circ}=\pi\\\\\\\dashrightarrow\sf\:\:1^{\circ}=\dfrac{\pi}{180^{\circ}}\\\\\\\dashrightarrow\sf\:\:\theta=\theta \times \dfrac{\pi}{180}\\\\\\\dashrightarrow\sf\:\:75^{\circ} = 75 \times \dfrac{\pi}{180} \\\\\\\dashrightarrow\:\:\underline{\boxed{\sf 75^{\circ} = \dfrac{5\pi}{12}}}$