Which side is tangent

The angle c is formed by the intersection of the hypotenuse h and the adjacent side a. We are interested in the relations between the sides and the angles of the right triangle. Let us start with some definitions. We will call the ratio of the opposite side of a right triangle to the hypotenuse the sine and give it the symbol sin.

The ratio of the adjacent side of a right triangle to the hypotenuse is called the cosine and given the symbol cos. Finally, the ratio of the opposite side to the adjacent side is called the tangent and given the symbol tan. We claim that the value of each ratio depends only on the value of the angle c formed by the adjacent and the hypotenuse.

To demonstrate this fact, let's study the three figures in the middle of the page. In this example, we have an 8 foot ladder that we are going to lean against a wall. The wall is 8 feet high, and we have drawn white lines on the wall and blue lines along the ground at one foot intervals.

The length of the ladder is fixed. If we incline the ladder so that its base is 2 feet from the wall, the ladder forms an angle of nearly Media outlet trademarks are owned by the respective media outlets and are not affiliated with Varsity Tutors.

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Just put in the angle and press the button. You can read more about sohcahtoa Move the mouse around to see how different angles in radians or degrees affect sine, cosine and tangent. In this animation the hypotenuse is 1, making the Unit Circle. You can still navigate around the site and check out our free content, but some functionality, such as sign up, will not work. If you do have javascript enabled there may have been a loading error; try refreshing your browser.

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