What is the value of (340*sin(15))/(sin(60)) ?

The value of (340*sin(15))/(sin(60)) is (510sqrt(2)-170sqrt(6))/3

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(340*sin(15))/(sin(60))

\frac{340 \cdot sin ( 1 5 ^{\circ} )}{sin ( 6 0 ^{\circ} )}

\frac{510 2 - 170 6}{3}

Solution steps

\frac{340 sin ( 1 5 ^{\circ} )}{sin ( 6 0 ^{\circ} )}

Rewrite using trig identities:

sin (1 5^{\circ}) = \frac{6 - 2}{4}

Use the following trivial identity:

sin (6 0^{\circ}) = \frac{3}{2}

= \frac{340 \cdot \frac{6 - 2}{4}}{\frac{3}{2}}

Simplify

\frac{340 \cdot \frac{6 - 2}{4}}{\frac{3}{2}} : \frac{510 2 - 170 6}{3}

= \frac{510 2 - 170 6}{3}

4 arctan (- 1)

cos (2) - cos (1)

\frac{tan ( 12 0 ^{\circ} ) + tan ( 4 5 ^{\circ} )}{1 - tan ( 12 0 ^{\circ} ) tan ( 4 5 ^{\circ} )}

tan (2) + tan (1)

\frac{5}{cos ( 9 0 ^{\circ} )}

What is the value of (340*sin(15))/(sin(60)) ?
The value of (340*sin(15))/(sin(60)) is (510sqrt(2)-170sqrt(6))/3