In an isosceles triangle with a base of 5 cm and a lateral side of 20 cm

| September 3, 2021 | education

In an isosceles triangle with a base of 5 cm and a lateral side of 20 cm, the bisector of the angle at the base is drawn. Find the length of this bisector.

By the property of the bisector, it divides the side into segments proportional to the adjacent sides.

BD / CD = AB / CD.

BD / CD = 20/5 = 4.

ВD = ВС – СD = 20 – СD.

(20 – CD) / CD = 4.

5 * CD = 20.

СD = 20/5 = 4 cm.

From vertex B we draw the height BH, which is also the median, since the triangle is isosceles. Then CH = AC / 2 = 5/2 = 2.5 cm.

From the triangle BCH, we determine the cosine of the angle BCH.

CosВСН = СН / ВС = 2.5 / 20 = 0.125.

In the triangle ADC, using the cosine theorem, we determine the length of AD.

АD ^ 2 = АС ^ 2 + СD ^ 2 – 2 * АС * СD * CosВССН.

AD ^ 2 = 25 + 16 – 2 * 5 * 4 * 0.125.

AD ^ 2 = 41 – 5 = 36.

AD = 6 cm.

Answer: The length of AD is 6 cm.



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