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To be able to solve a triangle, one needs to know all three sides and all three angles. A right-angled triangle has a value of 90 degrees. It is a triangle in which one edge is a right angle. The rapport that exists between the sides and the angles of a right-angled triangle forms the basis for trigonometry. Learn how to solve right angle trigonometry.

Trigonometric functions can be used to find unknown sides in right angles. The side that is opposite the right angle says “c,” is called the hypotenuse. The sides that are adjacent to the right angle are called legs, which are sides “a” and “b.” One side may be identified as the side adjacent to angle b and opposite angle a. Side b is adjacent to angle “a” and opposite to angle “b.”

Trigonometric Functions

We can define trigonometric functions in terms of an angle (other than the right angle), say angle t, and the lengths of the sides of the triangle. Usually, the adjacent side is closest to the angle o. The side that is in the opposite is the side across from the angle t.

The hypotenuse is usually the longest side, and it is opposite the right angle. When solving for a side that is missing from a right-angled triangle, but only the acute angle is given, you can use the following trigonometric functions.

  • For sine; sin t = opposite/ hypotenuse
  • For cosine; cos t = adjacent/ hypotenuse
  • For tangent; tan t = opposite/ adjacent

  • The first step to solving a missing side in a right triangle is to identify which sides and what angle is given and then choose the fitting function to solve the problem.

    The Pythagorean Theorem in Trigonometry Problems

    There are different ways to find out the missing information in a right triangle. The Pythagorean Theorem is one of the methods, and it states that a2 +b2=c2. For example, you have a right triangle in which “a” and “b” are the lengths, and c is the length of the hypotenuse.

    If you are given information about the length of any two sides, you can use the Pythagorean Theorem in finding the lengths. Once you have all the side lengths, you can work out all of the trigonometric functions.

    How to Solve Right angle triangle trigonometry by Evaluating the Trigonometric Function of a Right Triangle

    If you are given information of the length of one side of the triangle and an angle, you can find the other measurements; you can use one of the trigonometric functions sin, cos and tan to find the missing side length.

    A common mnemonic for recalling the trigonometric functions is SOHCAHTOA established from the first letters of sine is opposite over hypotenuse, cosine which is adjacent over hypotenuse and tangent is the opposite over adjacent.

    How to Solve Right-Angle Trigonometry by Inversing Trigonometric Functions

    For you to solve the missing acute angle, you will use the trigonometric functions as well as the inverse key on your calculator to solve for the angle, say angle a, given only two sides.

    Feel free to contact us for your trig homework solver today in case you encounter any challenges.

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