Find the area of an isosceles triangle, in which the lateral side is 4 √ 5 cm, and the radius
| January 25, 2021 | education
Find the area of an isosceles triangle, in which the lateral side is 4 √ 5 cm, and the radius of the circumscribed circle is 5 cm.
In the OBC triangle, by the cosine theorem, we define the cosine of the OBC angle.
OC ^ 2 = ОВ ^ 2 + ВС ^ 2 – 2 * ОВ * ВС * CosОВС.
25 = 25 + 80 – 2 * 5 * 4 * √5 * CosOBS.
40 * √5 * CosOBS = 80.
CosOBS = 2 / √5.
In a right-angled triangle ВСН, CosСВН = 2 / √5 = BH / BC.
BH = BC * 2 / √5 = 4 * √5 * 2 / √5 = 8 cm.
In a right-angled triangle BCH, according to the Pythagorean theorem, CH ^ 2 = BC ^ 2 – BH ^ 2 = 80 – 64 = 16.
CH = 4 cm, then AC = 2 * 4 = 8 cm.
Then Savs = BH * AC / 2 = 8 * 8/2 = 32 cm2.
Answer: The area of the triangle is 32 cm2.
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