In a right-angled triangle, the bisector of the smallest angle intersects the leg at an angle of 110 °.
| February 28, 2021 | education
In a right-angled triangle, the bisector of the smallest angle intersects the leg at an angle of 110 °. Find the acute angles of this triangle.
1. Let us introduce the designation of the vertices of the triangle ABC. Angle C = 90 °. ВK bisector.
Angle AKВ = 110 °.
2. Angle ВKС = 180 ° – 110 ° = 70 °.
3. Angle СVK = 180 ° – 90 ° – 70 ° = 20 °.
4. Since the bisector ВK divides the angle ABC into two equal parts, the angle ABK = angle СВK = 20 °.
5. Angle ABC = 20 ° + 20 ° = 40 °.
6. We calculate the value of the angle BAC: 180 ° – 90 ° – 40 ° = 50 °.
Answer: the angle BAC is 50 °, the angle ABC is 40 °.
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