Answer:
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.
