Question

The value of β is:60º45º90º30º75º​

Answer 1

Answer:

  60°

Step-by-step explanation:

The definition of cosine tells you ...

  cos(β) = 3/6 = 1/2

  β = arccos(1/2) . . . . use the inverse cosine function to find the angle

  β = 60°

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The ratio of side lengths in a 30°-60°-90° triangle (one of the "special" triangles), is ...

  1 : √3 : 2

The 2 : 1 ratio of longest to shortest side in this right triangle is a clue that the largest acute angle is 60°. It also tells you that x = √3 times the short side length, so is x = 3√3.