The ABC triangle is given by the coordinates of the vertices A (1; 3) B (2; 4) C (3; 3). Find the outer angle at vertex A.
July 22, 2021 | education
| For the solution, we use the formula for determining the length of a segment by the coordinates of points.
AB = √ (X2 – X1) ^ 2 + (Y2 – Y1) ^ 2 = √ (2 – 1) ^ 2 + (4 – 3) ^ 2 = √ (1 + 1) = √2 cm.
AC = √ (X2 – X1) ^ 2 + (Y2 – Y1) ^ 2 = √ (3 – 1) ^ 2 + (3 – 3) ^ 2 = √ (4 + 0) = 2 cm.
BC = √ (X2 – X1) ^ 2 + (Y2 – Y1) ^ 2 = √ (3 – 2) ^ 2 + (3 – 4) ^ 2 = √ (1 + 1) = √2 cm.
Since AB = BC, the triangle is isosceles.
The Pythagorean theorem holds in the triangle. AC ^ 2 = BC ^ 2 + AB ^ 2.
2 ^ 2 = (√2) ^ 2 + (√2) ^ 2.
4 = 4.
The triangle is rectangular, angle B = 90, then angle A = C = 45.
Then the outer angle at the vertex is A = 180 – 45 = 135.
Answer: The outside angle at vertex A is 135.
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.