In Triangle ABC ortho centre is O.if angle BAC=85 and angle BCA=75.Find the angle OAC
70
To find the angle OAC, we need to use the properties of angles in a triangle along with some knowledge about the orthocenter.
1. Recall that the orthocenter is the point where the altitudes of a triangle intersect. In triangle ABC, the orthocenter O is the intersection of the altitudes from vertices A, B, and C.
2. Since we know that angle BAC = 85 and angle BCA = 75, we can find the remaining angle, angle ABC, using the property that the sum of the angles in a triangle is 180 degrees.
Angle ABC = 180 - angle BAC - angle BCA
= 180 - 85 - 75
= 20 degrees
3. Now, let's examine triangle OAC. The angle OAC is formed by the altitude from vertex C and the line segment AC.
4. The altitude from vertex C is perpendicular to side AB. Recall that the property of perpendicular lines is that the angle between them is 90 degrees.
5. Since the altitude from vertex C is perpendicular to side AB, angle ACO is 90 degrees.
6. Therefore, angle OAC is equal to angle ABC minus angle ACO.
Angle OAC = Angle ABC - Angle ACO
= 20 - 90
= -70 degrees
Using the information provided, the angle OAC is -70 degrees.