The longer base of isosceles trapezoid is 12 cm. the side is 5 cm. the acute angle is 37º. find the shorter base.

  4 cm

Step-by-step explanation:

You may recognize that 37° is the smaller acute angle in a 3-4-5 right triangle. That is, each half of the shorter base will be 4 units shorter than each half of the longer base. The shorter base is ...

  12 cm - 2(4 cm) = 4 cm

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If you don't recognize that, you can figure it out using trigonometry. The relationship between angles and triangle sides in a right triangle is summarized in the mnemonic SOH CAH TOA. It reminds you that ...

  Cos = Adjacent/Hypotenuse

If you draw an altitude from where the side meets the short base, the side adjacent to the 37° angle will be the difference mentioned above. The hypotenuse of the triangle is the side of the trapezoid, 5 cm. The difference is ...

  cos(37°) = (difference in half-bases)/(5 cm)

  (difference in half-bases) = (5 cm)(cos(37°)) ≈ 4.0 cm

Then the shorter base is ...

  short base = 12 cm - 2(4 cm) = 4 cm.

step-by-step explanation:

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