The base of an isosceles triangle is 18 cm, and its base angle is 44. Find the rest of the sides and corners

| June 14, 2021 | education

The base of an isosceles triangle is 18 cm, and its base angle is 44. Find the rest of the sides and corners of the triangle.

Let an isosceles triangle ABC be given, the base of which is AC = 18 cm, and its angle BAC at the base is 44 °. By the property of the angles at the base of an isosceles triangle: ∠BAC = ∠BCA = 44 °. Since the sum of the angles in the triangle is 180 °, we get that ∠ABС = 180 ° – 2 ∙ 44 °; ∠ABС = 92 °. Let’s draw the ВC median to the base of the AC triangle. By the property of the median: ∠ВКА = 90 °, then by the definition of the cosine, we get cosA = AK: AB, but AK = AC / 2, then AB = (AC / 2): cosA; AB = 9: cos44 °; AB ≈ 12.51 (cm).
Answer: the unknown sides of the triangle are 12.51 cm long, and the unknown angles of the triangle are ∠BCA = 44 °, ∠ABС = 92 °.



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