You can confidently label the three interior angles because you see the relationships between the hypotenuse and short leg and the short leg and long leg.
Your knowledge of the 30-60-90 triangle will help you recognize this immediately. What is you have a triangle with the hypotenuse labeled 2,020 m m, the short leg labeled 1,010 m m, and the long leg labeled 1,010 3. It follows that the hypotenuse is 28 m, and the long leg is 14 m * 3. We know immediately that the triangle is a 30-60-90, since the two identified angles sum to 120 °: You can use the Pythagorean Theorem to check your work or to jump-start a solution.Ī right triangle has a short side with a length of 14 m e t e r s with the opposite angle measuring 30 °.
It is still a triangle, so its interior angles must add to 180 °, and its three sides must still adhere to the Pythagorean Theorem: Doubling this gives 18 3 for the hypotenuse.Īnother warning flag with 30-60-90 triangles is that you can become so engrossed in the three properties that you lose sight of the triangle itself. Unless your directions are to provide a decimal answer, this can be your final answer for the length of the short side. Multiply both numerator and denominator times 3: The rules of mathematics do not permit a radical in the denominator, so you must rationalize the fraction. You leap into the problem since getting the short leg is simply a matter of dividing the long leg by the square root of 3, then doubling that to get the hypotenuse.īut you cannot leave the problem like this: What if the long leg is labeled with a simple, whole number? You will notice our examples so far only provided information that would "plugin" easily using our three properties. Work carefully, concentrating on the relationship between the hypotenuse and short leg, then short leg and long leg. That relationship is challenging because of the square root of 3. When working with 30-60-90 triangles, you may be tempted to force a relationship between the hypotenuse and the long leg. This table of 30-60-90 triangle rules to help you find missing side lengths: 30-60-90 Triangle Rules If you know. You can create your own 30-60-90 Triangle formula using the known information in your problem and the following rules. The length of the hypotenuse is always twice the short leg's length. The long leg is the short leg times 3, so can you calculate the short leg's length? Did you say 5? We set up our special 30-60-90 to showcase the simplicity of finding the length of the three sides. We also know that the long leg is the short leg multiplied times the s q u a r e r o o t o f 3: We know that the hypotenuse of this triangle is twice the length of the short leg: Wisdom is knowing what to do with that knowledge. Two 30-60-90 triangles sharing a long leg form an equilateral triangleĮducation is knowing that 30-60-90 triangles have three properties laid out in the theorem.
Other interesting properties of 30-60-90 triangles are: