Parking Lot HW? Joke of the Day: What do you get when you combine a flat, infinite geometric figure with a beef patty? a plane burger Agenda 1 23 hw? Finish Special Right Triangles L8 3 Trig Ratios HW: L8 1 to 8 3 math xl Quiz Review Quiz: similarity & L8 1 to 8 3 Wednesday Goals: I can use patterns in special right triangles to solve problems I can use sine, cosine & tangent ratios to find side lengths & angle measures in right triangles. 1
HW Questions from Similarity Review #15 mathxl L8 1 2
How do you find the geometric mean of 2 numbers? 3
How many triangles do you see? 4
Short leg Short leg = long leg long leg How many triangles? Are they similar? 5
Think similar polygons What ratios can you write? 6
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think corresponding sides 8
mirror 9
Short Cuts using Special Right Triangles 10
Special Right Triangle investigation Name: 5. Without measuring, how long is the short leg of your triangle? 6. Calculate the length of the long leg of your special right triangle. Leave your answer in simplified radical form and record it in the table below. 7. Complete your table by sharing with your group. What patterns do you notice? 8. Find the missing sides of the following 30 60 90 triangles. 2 30 o 30 o 3 30 o 7 11
12. How can you determine the length of the short leg if you know the long leg? 13. Find the value of each variable in simplified radical form. 14. An equilateral triangle has a side length of 10 inches. What is the area? 12
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Complete 14 23 with your Team 14. Measure the side of your square with the paper ruler. 15. Cut the square in half along one diagonal. This makes a special right triangle. Based on the angles you just formed, it is called a triangle. 16. Use the pythagorean theorem to find the length of the hypotenuse of your right triangle in simplified radical form. small triangle medium triangle large triangle leg 1 leg 2 hypotenuse 17. Complete your table by sharing with your group. What patterns do you notice? 18. Since all 3 triangles are similar ( theorem) confirm the following ratios are the same for each triangle: leg hypotenuse leg 19. If you know the leg of a 45 45 90 triangle, how can you determine the hypotenuse? 20. If you know the hypotenuse of a 45 45 90 triangle, how can you find a leg? 21. complete the table below 14
22. Find the value of x. 23. A baseball diamond is actually a square. In baseball, the distance from home to first is 90 ft. In softball, it is 60ft. How much further does a catcher have to throw to second base in a baseball field? 24. 25. Find the values of the variables in simplest radical form. 15
In your notes: Special Right Triangle Short Cuts: the basic 30 60 90 the basic 45 45 90 16
L8 2 17
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L8 3 Trignometry How do you use sine, cosine, and tangent ratios to find side lengths and angle measures in right triangles? More short cuts for Right Triangles! 19
Trigonometry the study of triangle ratios 2 2 1 How are these 3 triangles related? 1 Find the following ratios for each triangle to 4 decimal places: leg hypotenuse leg leg 3 3 2 1 4 2 10 5 How are these 3 triangles related? Find the following ratios for each triangle to 4 decimal places: short leg short leg long leg long leg long leg hypotenuse hypotenuse short leg 20
can you find any of the ratios on this table? can you find any patterns? 21
How are the sides related to <T? Opposite across from Adjacent next to hypotenuse opposite right angle 22
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https://www.youtube.com/watch?v=piwjo5uk3fo 24
Now, you do it! B B' 3 5 C A 6 4 10 C' 8 A' sin(a) cos(a) tan(a) sin(b) cos(b) tan(b) 25
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How do the sides of the triangle relate to the given angle? 27
Use trig to find missing side: 35 o x 4 31 o 45 o x 5 28
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Using Inverses to find Angle Measures What do we know? So we should use... 30
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Find a missing angle using trig: If the sin(a) =.5, how big is angle A? If the sin(b) =.6, about how big is angle B? if: opp hyp then: sin 1 ( ) = adj hyp cos 1 ( ) = tan 1 opp ( ) = adj 33
find the missing angle 24 34
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some honors questions: What's the area of a square inscribed in a circle of radius 5"? What's the area of a regular hexagon inscribed in a circle of radius 20cm? What's the area of this trapezoid? 6 60 o 10 36