Solve 2sqrt{2}*sin(105^circ)divsin(30^circ)

$$2 \sqrt{ 2 } \times \sin ( 105 ^ { \circ } ) \div \sin ( 30 ^ { \circ } )$$

Evaluate

$$\frac{9659258262890683\sqrt{2}}{2500000000000000}\approx 5.464101615$$

Solution Steps

Evaluate trigonometric functions in the problem

$$2 \sqrt{2} \cdot 0.9659258262890683 / \sin(30)$$

Multiply 0.9659258262890683 and 2 to get 1.9318516525781366.

$$\frac{1.9318516525781366\sqrt{2}}{\sin(30)}$$

Get the value of \sin(30) from trigonometric values table.

$$\frac{1.9318516525781366\sqrt{2}}{\frac{1}{2}}$$

Divide 1.9318516525781366\sqrt{2} by \frac{1}{2} by multiplying 1.9318516525781366\sqrt{2} by the reciprocal of \frac{1}{2}.

$$1.9318516525781366\sqrt{2}\times 2$$

Multiply 1.9318516525781366 and 2 to get 3.8637033051562732.

$$3.8637033051562732\sqrt{2}$$