Right Triangle Trigonometry

1. Right Triangle Trigonometry Day 1

2. Pythagorean Theorem • Recall that a right triangle has a 90° angle as one of its angles. • The side that is opposite the 90° angle is called the hypotenuse. • The Pythagoreans theorem says that the square of the hypotenuse is equal to the sum of the squares of the legs. c2 = a2 + b2 a c b

3. Similar Triangles • Triangles are similar if two conditions are met: • The corresponding angle measures are equal. • Corresponding sides must be proportional. (That is, their ratios must be equal.) • The triangles below are similar. They have the same shape, but their size is different. A D c b f e E d F B a C

4. Example • Find the missing side lengths for the similar triangles. 3.2 3.8 y 54.4 x 42.5 x = (54.4)(3.8)/3.2 = 64.6 y = (42.5)(3.2)/54.4 = 2.5

5. Introduction to Trigonometry opp is the side opposite angle A • adj is the side adjacent to angle A • hyp is the hypotenuse of the right triangle hyp opp adj A

6. Define the three basic trigonometric ratios: sine, cosine and tangent. Just remember sohcahtoa! Sin Opp Hyp Cos Adj Hyp Tan Opp Adj -or-

7. During a trip to Italy, you visited a wonder of the world, the Leaning Tower of Pisa. Your guidebook explains that the tower now makes an 85 degree angle with the ground and measures 179 feet in height. If you drop a stone straight down from the top of the tower, how far from the base will it land?

9. Two acute angles are complementary if their sum is a right angle. and are complimentary angles c b a

10. Cofunctions of complimentary angles are equal c b a

11. Cofunctions of complimentary angles are equal

12. h 25 h = 23.49

13. *This time use the equivalent cofunction. h 25 h = 23.49