triangle ABC,angleA=60 degree,angleB=70 degree,angleC=50 degree. AB=6cm,BC=6.5cm,AC=7cm. Find its orthocentre.
To find the orthocenter of triangle ABC, we need to first understand what an orthocenter is. In a triangle, the orthocenter is the point where the three altitudes of the triangle intersect. An altitude is a line segment drawn from a vertex perpendicular to the opposite side.
To find the orthocenter of triangle ABC, we will follow these steps:
Step 1: Draw the triangle ABC with the given measurements.
- Start by drawing a line segment AB of length 6cm.
- From point B, draw line segment BC of length 6.5cm, making an angle of 70 degrees with AB.
- From point C, draw line segment CA of length 7cm, making an angle of 50 degrees with BC.
- Connect points A and C to form the sides of the triangle.
Step 2: Find the altitude of side AC.
- Draw a line segment from point B perpendicular to side AC.
- Label the point of intersection between this line and side AC as point D.
Step 3: Find the altitude of side BC.
- Draw a line segment from point A perpendicular to side BC.
- Label the point of intersection between this line and side BC as point E.
Step 4: Find the altitude of side AB.
- Draw a line segment from point C perpendicular to side AB.
- Label the point of intersection between this line and side AB as point F.
Step 5: Find the intersection of the three altitudes (orthocenter).
- To find the orthocenter, locate the intersection point of the three altitudes, which is the point of intersection of lines AD, BE, and CF.
- Label this point as point H.
Step 6: Verify your answer.
- Check if the lengths of AH, BH, and CH are perpendicular to sides BC, AC, and AB, respectively. If they are, then point H is indeed the orthocenter of triangle ABC.
By following these steps, you should be able to find the orthocenter of triangle ABC.