In a right-angled triangle, the bisector of a smaller angle forms angles with a smaller leg, one of which is 20 degrees less than the other. Find the sharp corners of the triangle.
The BDC angle is adjacent to the BDA angle, the sum of which is 180.
Angle BDC + BDA = 180.
By condition, the angle ВDА = ВDC + 20.
Then BDC * BDC + 20 = 180.
2 * ВDC = 160.
ВDC = 160/2 = 80.
The CBD triangle is rectangular, then the angle CBD = (90 – BDC) = (90 – 80) = 10.
Since BD is a bisector, then ABC = 2 * CBD = 2 * 10 = 20.
Then the angle BAC = (90 – ABC) = (90 – 20) = 70.
Answer: The acute angles of the triangle are 20 and 70.
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.