Area Of 30 60 90 Triangle Math

For a 30 60 90 triangle with hypotenuse of length a the legs have lengths b asin 60 degrees 1 2asqrt 3 1 c asin 30 degrees 1 2a 2 and the area is a 1 2bc 1 8sqrt 3 a 2. A 30 60 90 right triangle literally pronounced thirty sixty ninety is a special type of right triangle where the three angles measure 30 degrees 60 degrees and 90 degrees. The lengths of the sides of a 30 60 90 triangle are in the ratio of 1 3 2.

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The triangle is significant because the sides exist in an easy to remember ratio.

Area of 30 60 90 triangle math. The hypotenuse is 2a. 3 the inradius r and circumradius r are r 1 4 sqrt 3 1 a 4 r 1 2a. The perimeter equals a 3 3 the formulas are quite easy but what s the math behind them. How to solve a 30 60 90 triangle.

And because this is a 30 60 90 triangle and we were told that the shortest side is 8 the hypotenuse must be 16 and the missing side must be 8 3 or 8 3. In the study of trigonometry the 30 60 90 triangle is considered a special triangle knowing the ratio of the sides of a 30 60 90 triangle allows us to find the exact values of the three trigonometric functions sine cosine and tangent for the angles 30 and 60. In the figure above as you drag the vertices of the triangle to resize it the angles remain fixed and the sides remain in this ratio. See also side angle relationships of a triangle.

That is to say the hypotenuse is twice as long as the shorter leg and the longer leg is the square root of 3 times the shorter leg. It is right triangle whose angles are 30 60 and 90. If md 7cm calculate the area of triangle dnm. 30 60 90 triangle in trigonometry.

The area is equal to a 3 2. The following diagram shows a 30 60 90 triangle and the ratio of the sides. A special kind of triangle. Our final answer is 8 3.

30 60 90 triangle formula. In a right angle triangle abc with hypotenuse bc and c 60 degrees m and n are the middles of ab and ac respectively. Remembering the rules for 30 60 90 triangles will help you to shortcut your way through a variety of math problems. The 30 60 90 triangle is one example of a special right triangle.

Scroll down the page for more examples and solutions on how to use. Draw nd perpendicular to bc d is point on the side bc. Corollary if any triangle has its sides in the ratio 1 2 3 then it is a 30 60 90 triangle. The second leg is equal to a 3.

Assume that the shorter leg of a 30 60 90 triangle is equal to a. But do keep in mind that while knowing these rules is a handy tool to keep in your belt you can still solve most problems without them. For example sin 30 read as the sine of 30 degrees is the ratio of the side opposite the.