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Note that the hypotenuse is twice as long as the shortest leg which is opposite the 30° angle, so that.
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You can use this triangle (which is sometimes called a 30° - 60° - 90° triangle) to find all of the trigonometric functions for 30° and 60°. Here is the left half of the equilateral triangle turned on its side. You can determine the height using the Pythagorean Theorem. They both have a hypotenuse of length 2 and a base of length 1. If you split the equilateral triangle down the middle, you produce two triangles with 30°, 60° and 90° angles. Start with an equilateral triangle with side lengths equal to 2 units. You can construct another triangle that you can use to find all of the trigonometric functions for 30° and 60°. Notice that because the opposite and adjacent sides are equal, cosecant and secant are equal. Notice that because the opposite and adjacent sides are equal, sine and cosine are equal. Use the definitions of sine, cosine and tangent.
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However, you really only need to know the value of one trigonometric ratio to find the value of any other trigonometric ratio for the same angle.įind the values of the six trigonometric functions for 45° and rationalize denominators, if necessary. Some problems may provide you with the values of two trigonometric ratios for one angle and ask you to find the value of other ratios. You probably used the correct definition,, and used the Pythagorean Theorem to find the opposite side length, r, but set up the equation incorrectly. You need to know the opposite side length, so use the Pythagorean Theorem. Divide the hypotenuse by the opposite length. Use the Pythagorean Theorem to find the opposite side length. Remember that the two acute angles will give you different trigonometric function values. We memorize the 45 45 90 pattern so we can quickly recognize if a right triangle has two congruent legs and two 45 degree internal angles. It is also considered an isosceles triangle since it has two congruent sides. It looks like you used the wrong angle and found. A 45 45 90 triangle is a special right triangle with angles of 45, 45, and 90 degrees. Then divide the hypotenuse by the opposite length.