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Download Name: Period: Trigonometry Unit Lesson: Review Right Triangle
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Name: Period: Trigonometry Unit Lesson: Review Right Triangle Trigonometry Do Now What is a ray? Your Definition Draw a Ray What is a vertex? Your Definition Draw a Vertex What is an angle? Your Definition Draw an Angle What is a right angle? Your Definition Draw a Right Angle What is a right triangle? Your Definition Draw a Right Triangle Lesson What is a ray? Definition A ray is a part of a line that begins at a particular point (called the endpoint) and extends endlessly in one direction. “Half-line” What is a vertex? Definition The point where two endpoints of two rays intersect. What is an angle? Definition An angle is a combination of two rays (half-lines) with a common endpoint. Draw a Ray Draw a Vertex Draw an Angle What is a right angle? Definition An angle that measures 90 degrees. Draw a Right Angle What is a right triangle? Definition A triangle that has one angle that measures 90 degrees. Draw a Right Triangle Pythagorean’s Theorem Definition of Pythagorean’s Theorem Illustrate Pythagoreans Theorem A rule stating that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides. It is mathematically stated as c2 = a2 + b2, where c is the length of the hypotenuse and a and b the lengths of the other two sides. Problem 1 Suppose I have a right triangle. One leg is 6 inches. The other leg is 8 inches. What is the length of the hypotenuse? 10 Problem 2 Suppose I have a right triangle. The hypotenuse is 13 feet. One leg is 5 feet. What is the length of the other leg? 12 Does Pythagorean’s Theorem apply to all triangles? Why or why not? No- only right triangles have a hypotenuse Right Triangle Ratios Using this right triangle, label each leg as adjacent or opposite of angle x. Label the hypotenuse. Then, find sine, cosine, and tangent of angle x. Is there an easy way to remember these 3 ratios? SOHCAHTOA Practice 1) Draw a right triangle. Label one angle as a (do not label the right angle as a). Label the hypotenuse a 5. Label the leg opposite a as 4. Label the leg adjacent to a as 3. Then, find sine, cosine, and tangent of angle a. 2) Using the following right triangle, what is sine of angle a? What is cosine of angle a? What is tangent of angle a? What is sine of angle c? What is cosine of angle c? What is tangent of angle c?
