An isosceles triangle ΔABC with base AC = 15 cm is given. The segment BK is bisector, ∠ABK = 42 °. Find KC, ∠BAC and ∠BKA.

univerkov | March 11, 2021 | education

Since the triangle is isosceles, the bisector drawn from the angle not at the base is also the height and median.
Thus, the angle BKA = 90 °.
BK is the median, so AK = KC = AC / 2 = 15/2 = 7.5.

ABC = ABK * 2 = 42 ° * 2 = 84 °

BAC = BCA = (180 ° – 84 °) / 2 = 96 ° / 2 = 48 °
Answer: 7.5; 48 °; 90 °.

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