Height A is drawn in an isosceles triangle ABC. It is known that AB = 10, BK = 6.
| August 6, 2021 | education
Height A is drawn in an isosceles triangle ABC. It is known that AB = 10, BK = 6. Find the height AK and base AC if the angle B is obtuse.
The height of AK forms a right-angled triangle ABK, then, according to the Pythagorean theorem, AK ^ 2 = AB ^ 2 – BK ^ 2 = 100 – 36 = 64.
AK = 8 cm.
Since the triangle ABC is isosceles, then BC = AB = 10 cm.
The length of the segment CК = КВ + ВС = 6 + 10 = 16 cm.
Triangle CAK is rectangular, where, according to the Pythagorean theorem, we determine the length of AC.
AC ^ 2 = AK ^ 2 + CK ^ 2 = 64 + 256 = 320.
AC = 8 * √5 cm.
Answer: The length of the base of the speaker is 8 * √5 cm.
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