Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Unit 6.1 Tangent Ratio Standard: G.SRT.6 BellWork ∆QRS ~ ∆TUV. Find the value of x. Objective: To use basic trigonometric functions defined by the angles of a right triangle. Right Triangle There are three sides in a right triangle that need to be labeled by one of the acute angle, ____ (________). The side across the right angle is called the _______________, the side across of θ is called the _________ _____, and the side next to θ is called the __________ _____. Example 1 Label the right triangle’s sides according to θ. Checkpoint Label the right triangle’s sides according to θ. Similar Right Triangles Tangent Ratio ∆ABC ~ ∆GHI ~ ∆RST. Let’s investigate the ratio of the length of the opposite leg to the length of the adjacent leg. You may have discovered that in a right triangle, the ________ of congruent angles are __________. This ratio is called the tangent of the angle. Let ∆ABC be a right triangle with A and B. Example 2 Write the ratios for tan R and tan S. Checkpoint Write the ratios for tan X and tan Y. Example 3 Find the tan S and tan R. Write each ratio as a fraction and decimal. Checkpoint Find the tan D and tan F. Write each ratio as a fraction and decimal. Example 4 Find the length of AC. Checkpoint Find the length of RQ. Example 5 A long ladder is leaning against a building and makes an angle of 56° with the ground. The base of the ladder is 5 feet from the building. How far up the side of the building does the ladder reach? Checkpoint A slide makes a 38° angle with the ground. The base of the slide is 10 feet. How high is the top of the slide above the ground?