Mathematics
emilytaylor7256
2016-04-09 15:30:12
In the case of a triangle with angle measures of 30°, 60°, and 90° and a hypotenuse length equal to x, what is the perimeter of the triangle in terms of x?
ANSWERS
meronalbazzo
2016-04-09 16:43:54

Let "a" be a shorter leg (lies opposite to angle 30°), "b" is a longer leg (lies opposite to angle 60°), "c" is a hypotenuse (c = x). In the 30°-60°-90° triangle, the side lying opposite to the angle 30° is half the hypotenuse, so: [latex]a= frac{x}{2} [/latex] By the Pythagorean theorem: [latex]b^2 = c^2-a^2\ \b^2=x^2-( frac{x}{2} )^2 = x^2- frac{x^2}{4} = frac{4x^2-x^2}{4}= frac{3x^2}{4} \ \ b= sqrt{ frac{3x^2}{4} } = frac{ sqrt{3x^2} }{ sqrt{4} } = frac{x sqrt{3} }{2} [/latex] [latex] ext{Perimeter }=x+ frac{x}{2} + frac{x sqrt{3} }{2}= frac{2x+x+x sqrt{3}}{2}= frac{3x+x sqrt{3} }{2}[/latex]

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