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The sine of 120 degrees can be found using the unit circle. It is equivalent to sin(180° - 60°), which gives sin(120°) = sin(60°). Since sin(60°) is √3/2, the ratio for sin 120 degrees is √3/2.

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1w ago

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What is the perimeter of an isosceles triangle whose base angles add up to 60 degrees and has an area of 132.61014 square cm showing work?

Suppose the base of the triangle is of length x cm and the equal sides are of length y cm.The base angles sum to 60 degrees so each is 30 degrees and the apex angle is 180-60 = 120 degrees.Then area = 132.61014 = 0.5*y2*sin(120)So that y2 = 132.61014/[0.5*sin(120)] = 306.25and therefore, y = 17.5 cm.Then, by the sine rule, x/sin(120) = y/sin(30)So x = y*sin(120)/sin(30) = 30.31 cmAnd therefore, perimeter = x + 2*y = 65.31 cm.


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