Solving Right Triangles GEOMETRY Solving Right Triangles CONFIDENTIAL

Warm Up Use your calculator to find each trigonometric ratio. Round to the nearest hundredth. 1) sin 63˚ 2) cos 27˚ 3) tan 64˚ 1) 0.89 ; 2) 0.89 ; 3) 2.0503 CONFIDENTIAL

Right Triangles You can use trigonometric ratios to change a percent grade to an angle measure. CONFIDENTIAL

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. CONFIDENTIAL

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 CONFIDENTIAL

Inverse Trigonometric Functions CONFIDENTIAL

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

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 CONFIDENTIAL

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

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 CONFIDENTIAL

Solving a Right Triangle in the Coordinate Plane X 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  CONFIDENTIAL

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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° CONFIDENTIAL

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

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

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 CONFIDENTIAL

Now some practice problems for you! CONFIDENTIAL

Assessment Use the given trigonometric ratio to determine which angle of the triangle is /A . 1 2 CONFIDENTIAL

Use your calculator to find each angle measure to the nearest degree. 4) 5) 6) 650 710 380 CONFIDENTIAL

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 CONFIDENTIAL

⁄ 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° CONFIDENTIAL

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. CONFIDENTIAL

Inverse Trigonometric Functions CONFIDENTIAL

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

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

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

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

Solving a Right Triangle in the Coordinate Plane X 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  CONFIDENTIAL

X Y Next page  CONFIDENTIAL

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You did a great job today! CONFIDENTIAL