A triangular entraceway has walls with corner angles of 50, 70, 60. The designer wants to place a tall bronze sculpture on a round pedestal in a central location equidistant from the three walls. How can the designer find where to place the sculpture?
You would want the incentre of the triangle, which is the intersection of the angle bisector, and which is equidistant from each of the three sides.
So he should bisect any of the two angles and mark where these bisectors meet.
To find the central location equidistant from the three walls of the triangular entranceway, the designer can follow these steps:
1. Draw a diagram of the triangular entranceway, labeling the three corners with their respective angles: 50°, 70°, and 60°.
2. The central location equidistant from the three walls will be the intersection of the three perpendicular bisectors of the walls.
3. To find the perpendicular bisector of each wall, determine the midpoint of each wall segment. In this case, you will have three midpoints.
4. To construct the perpendicular bisector for each wall segment, use a compass and draw an arc with the midpoint as the center and any radius greater than half the length of the wall segment. The arc should intersect the wall segment at two points.
5. Repeat the process for the other two wall segments, creating arcs that intersect the respective wall segments.
6. Using a straight edge, draw lines connecting the intersections of the arcs on each wall segment. The point where the three lines intersect is the central location equidistant from the three walls.
7. The designer can place the tall bronze sculpture on a round pedestal at this central location to achieve a balanced and visually appealing arrangement.