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Find the length of side x in simplest radical form with a rational denominator.

Find The Length Of Side X In Simplest Radical Form With A Rational Denominator class=

Sagot :

Answer: 10

Step-by-step explanation:

a 30° - 60° - 90° triangle has a side ratio of 1:√3: 2, meaning the side length across from the 30° is 1, the side length across from 60° is √3, and the side length across from 90° is 2

if you multiple the 1 * 5 = 5 (the 5 side length in the diagram), then also multiple (5 * √3 = 5√3) and (2 * 5 = 10)

since you're looking for the hypotenuse (the length across the 90°), the answer would be 10 (2 * 5 = 10)

*this method can work for any 30° - 60° - 90° triangle

you can also use trig:

sin (30°) = [tex]\frac{5}{x}[/tex] (now just solve for x)

x * sin (30°) = 5

x = [tex]\frac{5}{sin(30)}[/tex]

x = [tex]\frac{5}{1/2}[/tex] ( because sin (30°) = 1/2 )

x = 5 * [tex]\frac{2}{1}[/tex] = 10

*either method works!