The height from a corner
Show on a big screenA sail is a triangle. How high is its top corner above the bottom edge? Draw a line from the corner, square to the bottom edge.
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The rule
The length of that line is the height. Where it meets the bottom edge is its foot. The legs are the two sides next to a right angle. To extend a side is to make it longer.
An altitude is the perpendicular from a corner to the opposite side. Extend that side if it is needed. Its length is the height. Look at the two corners on that side. If either is obtuse, the foot falls outside. If either is 90°, the foot lands on that corner. If both are acute, it falls inside. In a right-angled triangle, two altitudes are the legs.
Every triangle has three altitudes, one from each corner.
| Triangle | Altitudes |
|---|---|
| Acute-angled | All three are inside |
| Right-angled | Two are the legs. One is inside |
| Obtuse-angled | One is inside. Two fall outside |
The foot of a leg is the right-angle corner. In the lab, the dashed line is the side made longer.
Try the lab to finish this lesson.