What is the value of (100sin(30))/(sin(105)) ?

The value of (100sin(30))/(sin(105)) is 50sqrt(2)(sqrt(3)-1)

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(100sin(30))/(sin(105))

\frac{100 sin ( 3 0 ^{\circ} )}{sin ( 10 5 ^{\circ} )}

502 (3 - 1)

Solution steps

\frac{100 sin ( 3 0 ^{\circ} )}{sin ( 10 5 ^{\circ} )}

Use the following trivial identity:

sin (3 0^{\circ}) = \frac{1}{2}

Rewrite using trig identities:

sin (10 5^{\circ}) = \frac{2 ( 3 + 1 )}{4}

= \frac{100 \cdot \frac{1}{2}}{\frac{2 ( 3 + 1 )}{4}}

Simplify

\frac{100 \cdot \frac{1}{2}}{\frac{2 ( 3 + 1 )}{4}} : 502 (3 - 1)

= 502 (3 - 1)

20 \cdot tan (3 0^{\circ})

arcsin (\frac{6.3 sin ( 6 3 ^{\circ} )}{13})

- cos (π \cdot 0)

69.8 cos (74.04 4^{\circ})

9 5^{2} + 57.7 3^{2} - 2 \cdot 95 \cdot 57.73 sin (3 0^{\circ})

What is the value of (100sin(30))/(sin(105)) ?
The value of (100sin(30))/(sin(105)) is 50sqrt(2)(sqrt(3)-1)