In an isosceles triangle ABC AB = BC = 40 cm, AC = 20 cm. Point H is marked on side BC so that

| August 7, 2021 | education

In an isosceles triangle ABC AB = BC = 40 cm, AC = 20 cm. Point H is marked on side BC so that BH: HC = 3: 1. Find AH.

In an isosceles triangle ABC, we apply the cosine theorem and determine the value of the cosine of the angle ACB.

AB ^ 2 = AC ^ 2 + BC ^ 2 – 2 * AC * BC * CosACB.

1600 = 400 + 1600 – 2 * 20 * 40 * CosАСВ.

1600 * CosABS = 2000 – 1600.

CosАСВ = 400/1600 = 0.25.

Let the length of the segment CH = X cm, then the length of the segment BH = 3 * X cm.

Then BC = BH + CH = 3 * X + X = 40 cm.

4 * X = 40.

X = CH = 40/4 = 10 cm.

In the triangle ACN, by the cosine theorem, we define the length of the side AH.

AH ^ 2 = AC ^ 2 + CH ^ 2 – 2 * AC * CH * CosАСН = 400 + 100 – 2 * 20 * 10 * 0.25 = 500 – 100 = 400.

AH = 20 cm.

Answer: The length of the AH side is 20 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.