Find the area of triangle ABC, if it is known that point E divides BC into parts 4 cm and 12 cm, counting from vertex
| June 20, 2021 | education
Find the area of triangle ABC, if it is known that point E divides BC into parts 4 cm and 12 cm, counting from vertex B, angle ABC is 30 degrees, angle BAE is equal to angle ACB.
Consider triangles ABE and ABC.
According to the condition, the angle BAE = ACB, the angle B of the triangles is common.
Then triangles ABE and ABC are similar in two angles, the first sign of similarity of triangles.
From the similarity of triangles: AB / BC = BE / AB.
BC = BE + CE = 4 + 12 = 16 cm.
AB2 = BC * BC = 4 * 16 = 64.
AB = 8 cm.
Determine the area of the triangle ABC.
Savs = AB * BC * CosB / 2 = 8 * 16 * (1/2) / 2 = 32 cm2.
Answer: The area of the triangle is 32 cm2.
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