1. Check it out! 1 2.1.2: Exploring Sine and Cosine As Complements

2. The high school basketball team has won the division title, and a work crew is going to put a celebratory banner up on the gymnasium wall. The top of the banner will be 20 feet off the floor. The crew leader knows that the base of an extension ladder should be 7 feet away from the wall to form an angle of 76° with the floor. He is not sure if a 25-foot ladder will be long enough. 2 2.1.2: Exploring Sine and Cosine As Complements

3. 1.Create a drawing of this problem. 2.What side length needs to be found in order to determine if the ladder will be long enough to hang the banner so that the top of the banner is 20 feet off the floor? 3.Use the Pythagorean Theorem to find the height the ladder will reach on the wall. Will the ladder be long enough? 4.What is the measurement of ∠ A? 5.How does the sine of 75° compare to the cosine of 15°? 3 2.1.2: Exploring Sine and Cosine As Complements

4. 1.Create a drawing of this problem. 4 2.1.2: Exploring Sine and Cosine As Complements

5. 2.What side length needs to be found in order to determine if the ladder will be long enough to hang the banner so that the top of the banner is 20 feet off the floor? Length b needs to be found (the height on the wall). 5 2.1.2: Exploring Sine and Cosine As Complements

6. 3.Use the Pythagorean Theorem to find the height the ladder will reach on the wall. Will the ladder be long enough? The ladder will be long enough to reach the height of the banner on the wall. 6 2.1.2: Exploring Sine and Cosine As Complements

7. 4.What is the measurement of ∠ A? 7 2.1.2: Exploring Sine and Cosine As Complements

8. 5.How does the sine of 75° compare to the cosine of 15°? Using your calculator, find sin 75°. Using your calculator, find cos 15°. The sine of 75° and the cosine of 15° have exactly the same values. 8 2.1.2: Exploring Sine and Cosine As Complements