Solve c*sqrt{(33)^2+(60)^2-2(33)(60)cos60^circ}

$$c \cdot \sqrt { ( 33 ) ^ { 2 } + ( 60 ) ^ { 2 } - 2 ( 33 ) ( 60 ) \cos 60 ^ { \circ } }$$

Evaluate

$$3\sqrt{301}c$$

Solution Steps

Calculate 33 to the power of 2 and get 1089.

$$c\sqrt{1089+60^{2}-2\times 33\times 60\cos(60)}$$

Calculate 60 to the power of 2 and get 3600.

$$c\sqrt{1089+3600-2\times 33\times 60\cos(60)}$$

Add 1089 and 3600 to get 4689.

$$c\sqrt{4689-2\times 33\times 60\cos(60)}$$

Multiply 2 and 33 to get 66.

$$c\sqrt{4689-66\times 60\cos(60)}$$

Multiply 66 and 60 to get 3960.

$$c\sqrt{4689-3960\cos(60)}$$

Get the value of \cos(60) from trigonometric values table.

$$c\sqrt{4689-3960\times \frac{1}{2}}$$

Multiply 3960 and \frac{1}{2} to get 1980.

$$c\sqrt{4689-1980}$$

Subtract 1980 from 4689 to get 2709.

$$c\sqrt{2709}$$

Factor 2709=3^{2}\times 301. Rewrite the square root of the product \sqrt{3^{2}\times 301} as the product of square roots \sqrt{3^{2}}\sqrt{301}. Take the square root of 3^{2}.

$$c\times 3\sqrt{301}$$