1. Solving Right Triangles
GEOMETRY
Solving Right Triangles
CONFIDENTIAL

2. Warm Up
Use your calculator to find each trigonometric ratio. Round to the nearest hundredth.
1) sin 63˚ ) cos 27˚ ) tan 64˚
1) 0.89 ; 2) 0.89 ; 3)
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3. Right Triangles
You can use trigonometric ratios to change a percent grade to an angle measure.
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4. Angles from Trigonometric Ratios
Use the trigonometric ratio cos A = 0.6 determine which angle of the triangle is /A.
Cosine is the ratio of the adjacent leg to the hypotenuse.
The leg adjacent to /1 is 3.6. The hypotenuse is 6.
The leg adjacent to /2 is 4.8. The hypotenuse is 6.
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5. Now you try!
Use the given trigonometric ratio to determine which angle of the triangle is /A.
1a) 2
1b) 1
1a) sin A = 8/17
1b) tan A = 1.875
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6. Inverse Trigonometric Functions
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7. Calculating Angle Measures from Trigonometric Ratios
Use your calculator to find each angle measure to the nearest degree.
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8. Use your calculator to find each angle measure to the nearest degree.
Now you try !
Use your calculator to find each angle measure to the nearest degree.
36.87
87.13
42.07
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9. Solving Right Triangles
Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.
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10. Now you try!
Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.
⁄ D = 32°; EF = 8.75
DF = 16.5
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11. Solving a Right Triangle in the Coordinate PlaneX Y
The coordinates of the vertices of ∆JKL are J(-1,2), K(-1,-3), and L(3,-3). Find the side lengths to the nearest hundredth and the angle measures to the nearest degree.
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12. CONFIDENTIAL

13. Now you try!
The coordinates of the vertices of ∆RST are R(-3,5), S(4,5), and T(4,-2). Find the side lengths to the nearest hundredth and the angle measures to the nearest degree.
RS = 7; ST = 7; RT = 7√2
⁄R = 45° ; ⁄T = 45°
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14. Travel Application
San Francisco’s Lombard Street is known as one of “the crookedest streets in the world.” The road’s eight switchbacks were built in the 1920s to make the steep hill passable by cars. If the hill has a percent grade of 84%, what angle does the hill make with a horizontal line? Round to the nearest degree.
84 % = 84/100
Change the percent grade to a fraction
An 84% grade means the hill rises 84 ft for every 100 ft of horizontal distance.
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15. Draw a right triangle to represent the hill
Draw a right triangle to represent the hill. /A is the angle the hill makes with a horizontal line.
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16. Now you try!
Baldwin St. in Dunedin, New Zealand, is the steepest street in the world. It has a grade of 38%. To the nearest degree, what angle does Baldwin St. make with a horizontal line?
89.430
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17. Now some practice problems for you!
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18. Assessment
Use the given trigonometric ratio to determine which angle of the triangle is /A . 1 2
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19. Use your calculator to find each angle measure to the nearest degree.4) 5) 6)
650
710
380
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20. Multi-Step Find the unknown measures
Multi-Step Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. 7) 8)
⁄ R = 71°; ⁄ P = 19°; RP = 9.42
⁄ C = 58°; AB = 6.28; BC = 3.92
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21. ⁄ D = 63°; ⁄ F = 27°; DE = 3; EF = 6; DF = 3√5 5°
9) Find the side lengths to the nearest hundredth and the angle measures to the nearest degree for the given triangle.
D(4,1), E(4,-2), F(-2,-2)
10) A hill in the Tour de France bike race has a grade of 8%. To the nearest degree, what is the angle that this hill makes with a horizontal line?
⁄ D = 63°; ⁄ F = 27°; DE = 3; EF = 6; DF = 3√5 5°
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22. Angles from Trigonometric Ratios
Let’s review
Angles from Trigonometric Ratios
Use the trigonometric ratio cos A = 0.6 determine which angle of the triangle is /A.
Cosine is the ratio of the adjacent leg to the hypotenuse.
The leg adjacent to /1 is 3.6. The hypotenuse is 6.
The leg adjacent to /2 is 4.8. The hypotenuse is 6.
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23. Inverse Trigonometric Functions
CONFIDENTIAL

24. Calculating Angle Measures from Trigonometric Ratios
Use your calculator to find each angle measure to the nearest degree.
CONFIDENTIAL

25. Solving Right Triangles
Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.
CONFIDENTIAL

26. Travel Application
San Francisco’s Lombard Street is known as one of “the crookedest streets in the world.” The road’s eight switchbacks were built in the 1920s to make the steep hill passable by cars. If the hill has a percent grade of 84%, what angle does the hill make with a horizontal line? Round to the nearest degree.
84 % = 84/100
Change the percent grade to a fraction
An 84% grade means the hill rises 84 ft for every 100 ft of horizontal distance.
Next page 
CONFIDENTIAL

27. Draw a right triangle to represent the hill
Draw a right triangle to represent the hill. /A is the angle the hill makes with a horizontal line.
CONFIDENTIAL

28. Solving a Right Triangle in the Coordinate PlaneX Y
The coordinates of the vertices of ∆JKL are J(-1,2), K(-1,-3), and L(3,-3). Find the side lengths to the nearest hundredth and the angle measures to the nearest degree.
Next page 
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29. X Y
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30. CONFIDENTIAL

31. You did a great job today!
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