Geometry One is always a long way from solving a problem until one actually has the answer. Stephen Hawking Today: ACT VOCAB CHECK 8.4 Cont. Practice

Geometry Assignment: 8.4 p 573 #1-6, 28-35 Homework Quiz Monday One is always a long way from solving a problem until one actually has the answer. Stephen Hawking Assignment: 8.4 p 573 #1-6, 28-35 Homework Quiz Monday Test Chapter 8 Wednesday

ACT CHECK UP: Orange or Blue Which trig ratio is defined as : adjacent hypotenuse ORANGE BLUE COSINE SINE

ACT CHECK UP: Orange or Blue What is tan K? ORANGE BLUE 8/15 8/17

ACT CHECK UP: Orange or Blue Which trig ratio is defined as : opposite hypotenuse ORANGE BLUE COSINE SINE

ACT CHECK UP: Orange or Blue When the angle of elevation of the sun is 50°, a flagpole casts a 16.8 foot shadow. Find the height of the flagpole. ORANGE BLUE 14 ft 20 ft

ACT CHECK UP: Orange or Blue Which trig ratio is defined as : opposite adjacent ORANGE BLUE COSINE TANGENT

8.4 Solving Right Triangles Objectives: Applying Trig Ratios to Solve Right Triangles Use Trig Ratios in Real Life Examples   Vocabulary: Solving a Right Triangle

Mathematical Practices Content Standards G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles. Mathematical Practices 1 Make sense of problems and persevere in solving them. 5 Use appropriate tools strategically. CCSS

Find trigonometric ratios using right triangles. You used the Pythagorean Theorem to find missing lengths in right triangles. Find trigonometric ratios using right triangles. Use trigonometric ratios to find angle measures in right triangles. Then/Now

8.4 Solving Right Triangles To solve a right triangle: determine all six parts of the triangle. This includes: a right angle, two acute angles and all three sides. What does this triangle still need in order to be solved? 30° 8

8.4 Solving Right Triangles Solve the right triangle. Round any decimals to the nearest tenth. Where should we start?

8.4 Solving Right Triangles Solve the right triangle. Round any decimals to the nearest tenth. Next?

8.4 Solving Right Triangles Solve the right triangle. Round any decimals to the nearest tenth. Final Answer?

8.4 Solving Right Triangles Solve the right triangle. Round any decimals to the nearest tenth. Where should we start?

8.4 Solving Right Triangles Solve the right triangle. Round any decimals to the nearest tenth. Next? New idea: Find the measure of each acute angle. Still set up a trig ratio.

8.4 Solving Right Triangles A plane must clear a building near the end of the runway that is 80 feet high. If the building is 100 feet from the end of the plane, what does the angle of elevation at take off need to be? How many feet does the plane have to clear the building? DRAW A PICTURE!!!

ACT CHECK UP: Orange or Blue Which would find the mU? ORANGE BLUE sin-1(7.5/19.5) sin(7.5/19.5)

ACT CHECK UP: Orange or Blue Which angle has a cosine of 3/5? ORANGE BLUE A B

ACT CHECK UP: Orange or Blue A wheelchair ramp has a rise of 1 foot and a horizontal length of 14 feet. Find the angle the ramp makes with the ground. ORANGE BLUE 4° 6°

Things to Know

Trigonometric Ratios Set up sine, cosine, and tangent ratios as fractions Find side lengths using trigonometric ratios 11 a b 67°

Make sure you are in “Degree” Mode!!! Then use a calculator to find the measure of B: 2nd function m B ≈ 33.7° Make sure you are in “Degree” Mode!!!

Ratio Angle (degrees) sin A = x sin-1 x = mA Ratio Angle (degrees)

Solving Right Triangles Solve for all three sides and all three angles of a triangle Use inverse trigonometry to determine angle measures of triangles

Special Right Triangles Rule for special right triangles Simplify answers in radical form Use characteristics of special right triangles to solve for side lengths

Geometry Assignment: 8.4 p 575 #43, 44, 53, 62, 64, 66, 69 One is always a long way from solving a problem until one actually has the answer. Stephen Hawking Assignment: 8.4 p 575 #43, 44, 53, 62, 64, 66, 69 Homework Quiz Monday Test Chapter 8 Wednesday

Geometry Today: Homework Quiz ??????? Practice One is always a long way from solving a problem until one actually has the answer. Stephen Hawking

Geometry 8.4 p 575 #43, 44, 53, 62, 64, 66, 69 Assignment: One is always a long way from solving a problem until one actually has the answer. Stephen Hawking Assignment: 8.4 p 575 #43, 44, 53, 62, 64, 66, 69 Homework Quiz Monday Test Chapter 8 Wednesday

Geometry Assignment: Review Chapter 9 p. 610 #11-35 One is always a long way from solving a problem until one actually has the answer. Stephen Hawking Assignment: Review Chapter 9 p. 610 #11-35 Test Chapter 8 on Wednesday