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How do you find both legs of a triangle with only the hypotenuse?
You can't. The hypotenuse alone isn't enough to tell you anything about the lengths of the legs. There are an infinite number of different right triangles that all have the same hypotenuse but different legs.
What does the pythagorean theorem tell you?
In a right angle triangle the square of the hypotenuse is equal to height squared plus base squared
How do you find the height of a triangle if you only have the hypotenuse?
You can't. The hypotenuse alone isn't enough to tell you anything about the triangle. There are an infinite number of different right triangles that all have the same hypotenuse. In order to find anything else, you also need to know either the length of one leg, or else the size of one acute angle.
How can you tell from the angle measures of a triangle which side of the triangle is longest and shortest?
The smaller the angle, the smaller the side opposite it.
What is the area of an equilateral triangle with an apothem of 5cm?
5.7735 cm is the length of a side so 1/2 x base x Height should give you an answer. Remember, the apothem makes two mirrored 30 60 right triangles...Pythagoras will tell you how to find the hypotenuse...that will be the unknown side of the equilateral.
