In an isosceles triangle ABC, where AB = BC = 30 cm, the cosine of angle B is 0.8. Find the area of the triangle.

In an isosceles triangle ABC it is known:
AB = BC = 30 cm;
cos B = 0.8.
Find the area of the triangle.
Decision:
1) Find the side of the AС using the cosine theorem.
AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * cos B;
AC = √ (AB ^ 2 + BC ^ 2 – 2 * AB * BC * cos B);
AC = √ (30 ^ 2 + 30 ^ 2 – 2 * 30 * 30 * 0.8) = √ (900 + 900 – 900 * 1.6) = √ (1800 – 1440) = √360 = (36 * 10) = 6√ ten;
2) BK – height;
AK = 6√10 / 2 = 3√10;
ВK = √ (30 ^ 2 – (3√10) ^ 2) = √ (900 – 9 * 10) = √ (900 – 90) = √810 = √ (81 * 10) = 9√10;
3) S = 1/2 * AC * BK = 1/2 * 6√10 * 9√10 = 3√10 * 9√10 = 3 * 9 * 10 = 27 * 10 = 270.
Answer: S = 270.