Respuesta :

sqdancefan

Answer:

  [tex]\textbf{B. }\ \dfrac{3}{2}\sqrt{2}[/tex]

Step-by-step explanation:

You know the short side of an isosceles right triangle is 1/√2 times the hypotenuse. So, the hypotenuse of the 30°-60°-90° right triangle is ...

  6/√2 = (6√2)/2 = 3√2

You also know the short leg of a 30°-60°-90° right triangle is half the length of its hypotenuse, so ...

  x = (1/2)(3√2)

  x = (3/2)√2

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Additional comment

For many trig and geometry problems, it is useful to remember the ratios of side lengths for "special" right triangles:

  isosceles right triangle: 1 : 1 : √2

  30°-60°-90° triangle: 1 : √3 : 2     (shortest to longest)

This knowledge usefully relates to the trig function values for these "special" triangles.

mhanifa

Answer:

3/√2 or 3√2/2

Step-by-step explanation:

Bigger triangle has internal angles 45/45/90, so the legs have equal length and = 6/√2 as hypotenuse = 6

Smaller triangle has hypotenuse of 6/√2 and the angle against leg x is 30°

As we know the leg opposite to 30° angle is half the hypotenuse, so

  • x= 1/2*6/√2= 3/√2= 3√2/2

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