How would you construct an isosceles triangle if only given the altitude to the base and a base angle?

Answer 1

Start with the altitude (height) and draw that. Draw the actual length of the altitude on your paper, or draw it to scale. Naturally you'll draw it down the middle of your paper parallel to the sides (perpendicular to the bottom) of your paper. Now that you have your altitude, draw a line perpendicular to it across the bottom. Your base will be on that, but we don't know how big it is yet. Let's work with your base angle, but indirectly. You have a vertical line perpendicular to another line. There are two right angles formed, one on each side of the vertical line. If you could draw in one side of your isosceles triangle, you'd have a right triangle that represents half your isosceles triangle. The altitude divides your isosceles triangle exactly in half down the middle. This right triangle will, like all triangles, have interior angles that add up (sum) to 180 degrees. Now we use the base angle. You have the 90 degree angle, and the base angle. That base angle and the "top" angle will add up to 90 degrees, and that's so that these two angles and the 90 angle where the altitude meets the base will add up to 180 degrees. That means the base angle and the top angle will have to add up to 90 degrees. Subtract your base angle from 90 degrees and you'll have your "top" angle. Get you protractor, place it at the top of your altitude, and mark the "top" angle. Now draw a line from the top of the altitude on this angle you set, and continue it to the base. That's one side of your triangle. Repeat this on the other side and your isosceles triangle will appear.