Geom- Chpt. 8 Algebra Review Before the Chapter

Transcription

1 Geom- Chpt. 8 Algebra Review Before the Chapter Solving Quadratics- Using factoring and the Quadratic Formula Solve: 1. 2n 2 + 3n - 2 = 0 2. (3y + 2) (y + 3) = y x 2 13x = 32 1

2 Working with Radicals- Simplifying Radicals:

3 Geom- 8-1 Geometric Mean In class lesson Find the geometric mean Geometric Mean In Right Triangles There are 3 similar triangles in the triangle below. Pull out the triangles and then write the similarity statement. Altitude Geometric Mean Relationship Leg Geometric Mean Relationship 3

4 Flipped Classroom Video Example Problems

5 Geom- 8-2 The Pythagorean Theorem and Its Converse What is Pythagorean Theorem? You can use the Pythagorean theorem to determine if a triangle is a right, acute or obtuse triangle. Right Triangle Obtuse Triangle Acute Triangle 5

6 Determine whether the following sides can make a triangle and if it is a right, acute or obtuse triangle. 3. Pythagorean Theorem Triples: Examples of Pythagorean Triples: Use Pythagorean triples to solve the following. 4. 6

7 Geom- 8-3 Special Right Triangles Triangle relationships The formulas or relationship are derived from a square Triangle relationships The formulas or relationship are derived from an equilateral triangle. 7

8 Example problems

9 Geom- 8-4 Trigonometry In class Find the value of the variable Why are we not able to solve this one? Every single triangle has a special relationship. These special relationship are store in our calculator as trig ratios. Demonstrations. 9

10 Trig Functions- Soh - Cah Toa You must know the trig functions! B 4.37 cm 8.03 cm 90 A cm C Write the ratio for the following Sin C Find the value of Sin 33 Cos C Find the value of Cos 33 Tan C Find the value of Tan 33 10

11 Geom- 8-4 Trigonometry Flipped Classroom Video We will use the right triangle trigonometry to find the value of the variable(s)

12 Geom- 8-5 Angles of Elevation and Depression Many real-world problems that involve looking up to an object can be described in terms of an angle of elevation, which is the angle between an observer s line of sight and a horizontal line. When an observer is looking down, the angle of depression is the angle between the observer s line of sight and a horizontal line. Example problems. 1. TOWN ORDINANCES The town of Belmont restricts the height of flagpoles to 25 feet on any property. Lindsay wants to determine whether her school is in compliance with the regulation. Her eye level is 5.5 feet from the ground and she stands 36 feet from the flagpole. If the angle of elevation is about 25,what is the height of the flag pole to the nearest tenth? 2. SKIING A ski run is 1000 yards long with a vertical drop of 208 yards. Find the angle of depression from the top of the ski run to the bottom. 12

13 3. AIR TRAFFIC From the top of a 120- foot- high tower, an air traffic controller observes an airplane on the runway at an angle of depression of 19. How far from the base of the tower is the airplane? 4. Mrs. Hefty is in a satellite, which is 25 miles above a river and is on one side of the river. She notes an angle of depression of 40 degree to the near side of the river and a 37 degree angle to the far side. How wide is the river? 13

14 Geom- 8-6 The Law of Sines day 1 When we do not have a right triangle we still find the length of the sides and the measures of the angles. We will use Law of Sines to do this. What is law of sines and where does it come from? Law of Sines- Use this when you have the angle side opposite relationship in a triangle. Do not use this in right triangle! Yes it works but we will use right triangle trigonometry!!!! 14

15 Example Problems Find the missing measure. Round angles to nearest degree and sides to the tenths

16 Geom- 8-6 The Law of Cosines day 2 When do we use the law of sines? Law of Cosines: Use law of cosines when: Example Problems:

17 3. 17

18 Geom- 8-6 The Law of Sines & Cosines day 3 Word Problems 1. MAPS Three cities form the vertices of a triangle. The angles of the triangle are 40, 60, and 80. The two most distant cities are 40 miles apart. How close are the two closest cities? Round your answer to the nearest tenth of a mile. 2. CARS Two cars start moving from the same location. They head straight, but in different directions. The angle between where they are heading is 43 degrees. The first car travels 20 miles and the second car travels 37 miles. How far apart are the two cars? Round your answer to the nearest tenth. 18