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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 the opposite side to the adjacent side.The simplest triangle you can use that has that ratio is shown.
One way to remember this triangle is to note that the hypotenuse is You can construct another triangle that you can use to find all of the trigonometric functions for 30° and 60°.
Start with an equilateral triangle with side lengths equal to 2 units.
Remember that you have to use the keys 2ND and TAN on your calculator.
Look at the hundredths place to round to the nearest tenth. You may have been confused as to which ratio corresponds to which trigonometric function.
If you split the equilateral triangle down the middle, you produce two triangles with 30°, 60° and 90° angles. They both have a hypotenuse of length 2 and a base of length 1.
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°.Note that the hypotenuse is twice as long as the shortest leg which is opposite the 30° angle, so that .The length of the longest leg which is opposite the 60Since we know all the measures of the angles, we now need to find the lengths of the missing sides.Solving the equation and rounding to the nearest tenth gives you Sometimes you may be given enough information about a right triangle to solve the triangle, but that information may not include the measures of the acute angles.In this situation, you will need to use the inverse trigonometric function keys on your calculator to solve the triangle.Let’s look at how to do this when you’re given one side length and one acute angle measure.Once you learn how to solve a right triangle, you’ll be able to solve many real world applications – such as the ramp problem at the beginning of this lesson – and the only tools you’ll need are the definitions of the trigonometric functions, the Pythagorean Theorem, and a calculator. Substitute the measure of the angle on the left side of the equation and use the triangle to set up the ratio on the right.In the example above, you were given one side and an acute angle.In the next one, you’re given two sides and asked to find an angle. Remember that the two acute angles will give you different trigonometric function values.Use the Pythagorean Theorem to find the opposite side length. The correct answer is 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.