Pythagorean Theorem & Trigonometric Ratios

1 Algebra 2012-2013 Pythagorean Theorem & Trigonometric Ratios Name:_____ Teacher:_____ Pd: _____ Table of Contents DAY 1: SWBAT: Calculate the length of a side a right triangle using the Pythagorean Theorem Pgs: 1 - 4 HW: 5 - 6 DAY 2: SWBAT: Find the three basic Trigonometric Ratios in a right triangle Pgs: 7 - 10 HW: 11 - 12 DAY 3: SWBAT: Use Trigonometric Ratios to find missing lengths of a right triangle Pgs: 13 - 17 HW: 18 -19 DAY 4: SWBAT: Use Trigonometric Ratios to find a missing angle of a right triangle Pgs: 20 - 23 HW: 24 - 25 Day 5-6: Review Pgs: 26 - 32 Day 7: Test trig Overall Notes Pgs: 33 - 341 SWBAT: Calculate the length of a side a right triangle using the Pythagorean Theorem Pythagorean Theorem Day 1 Warm Up Introduction.

2 Over 2,500 years ago, a Greek mathematician named Pythagoras popularized the concept that a relationship exists between the hypotenuse and the legs of right triangles and that this relationship is true for all right triangles. Thus, it has become known as the Pythagorean Theorem . **SHOW SKETCHPAD ANIMATION ** Identify Pythagorean Theorem 222cba 2 Example 1: Find the value of x in the following diagrams. Round to the nearest tenth if necessary. A) B) Practice Problems: Find the value of x in the following diagrams.

3 Round to the nearest tenth if necessary. 1) 2) 3) 4) 5) 6) 8 15 x x 48 52 20 x 29 5 12 x x 8 10 8 x 12 3 Example 2: Pythagorean Theorem Word Problems A 15 foot ladder is leaning against a wall. The foot of the ladder is 7 feet from the wall. How high up the wall is the ladder? Practice Problems: Pythagorean Theorem Word Problems 7) If the length of a rectangular television screen is 20 inches and its height is 15 inches, what is the length of its diagonal, in inches? 8) An 18-foot ladder leans against the wall of a building.

4 The base of the ladder is 9 feet from the building on level ground. How many feet up the wall, to the nearest tenth of a foot, is the top of the ladder? 9) A cable 20 feet long connects the top of a flagpole to a point on the ground that is 16 feet from the base of the pole. How tall is the flagpole? 4 10) Regents Problem Challenge Problem In the accompanying diagram of right triangles ABD and DBC, AB = 5, AD = 4, and CD = 1. Find the length of ,BC to the nearest tenth.

5 Summary: Exit Ticket: 5 Homework - Pythagorean Theorem Day 1 Directions: Find the length of the missing side in the following examples. Round answers to the nearest tenth, if necessary. 6 7 SWBAT: Find the three basic Trigonometric Ratios in a right triangle Trigonometric Ratios Day 2 Warm Up Two joggers run 8 miles north and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile, they must travel to return to their starting point?

6 _____ SOH CAH TOA8 Example 2: SOH CAH TOA9 Practice Problems: 7) 8) Example 3 Practice (for example 3) SOH CAH TOA10 Challenge Problem: Summary: Exit Ticket: 11 Homework - Trigonometric Ratios Day 2 Write the ratio that represents the Trigonometric function in simplest form. 12 13 SWBAT: Use Trigonometric Ratios to find missing lengths of a right triangle Trigonometry: Solving for a missing Side - Day 3 Warm Up Determine the Trigonometric Ratios for the following triangle: (a) Sin A = (b) Cos A = (c) Tan A = (d) Sin B = (e) Cos B = (f) Tan B = Example 1: Determine the length of side x and y of each right triangle using Trigonometric Ratios .

7 Trigonometric Ratios Recall that in a right triangle with acute angle A, the following Ratios are defined: 12 15 20 yA B C 14 Practice Problems: Determine the length of side x and y of each right triangle using Trigonometric Ratios . Example 2: Determine the length of side x of each right triangle using Trigonometric Ratios . y15 h Practice 1) A ladder leans against a building as shown in the picture below. The ladder makes an acute angle with the ground of 72.

8 If the ladder is 14 feet long, how high, h, does the ladder reach up the wall? Round your answer to the nearest tenth of a foot. 2) 14 feet 16 3) A 14 foot ladder is leaning against a house. The angle formed by the ladder and the ground is72. (a) Determine the distance, d, from the base of the ladder to the house. Round to the nearest foot. (b) Determine the height, h, the ladder reaches up the side of the house. Round to the nearest foot. 4) In the accompanying diagram, x represents the length of a ladder that is leaning against a wall of a building, and y represents the distance from the foot of the ladder to the base of the wall.

9 The ladder makes a 60 angle with the ground and reaches a point on the wall 17 feet above the ground. Find the number of feet in x and y. Challenge Problem: d 72 14 ft h x 17 17 Summary Exit Ticket: 18 Homework - Trigonometry: Solving for a missing Side - Day 3 Directions: In problems 1 through 3, determine the Trigonometric ratio needed to solve for the missing side and then use this ratio to find the missing side.

10 1) In right triangle ABC, mAAB 588 and . Find the length of each of the following. Round your answers to the nearest tenth. (a) AC (b) BC (Hint: Use Pythagorean s Thm) 2) In right triangle ABC, mBAB 4415 and . Find the length of each of the following. Round your answers to the nearest tenth. (a) AC (b) BC (Hint: Use Pythagorean s Thm) 3) In right triangle ABC, mCAB 3224 and.