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Since the vertex angle is 64⁰, the base angle is 58⁰, (180⁰ - 64⁰ )/2.

Using the Law of Sines we have

side length/sin 58⁰ = 3 cm/sin 64⁰ (multiply by sin 58⁰ to both sides)

side length = (3 cm)(sin 58⁰)/sin 64⁰ ≈ 2.8 cm

Thus, the congruent sides of the given isosceles triangle have a length of 2.8 cm.

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Q: The base of an isosceles triangle is 3 cm in lenght and the angle opposite the base measure 64 degrees Find the lenght of each of the component sides?
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