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Geometry – Warm Up Right Triangles Day 8 Name _____________ Date _____________ Use the following diagram. Round decimals to the nearest tenth. P q r Q p R 1. If PR = 12 and m R = 19° solve the right triangle. GEOMETRY: Unit 7 (Chapter 7) Right Triangles Unit Review WHAT DO YOU NEED TO KNOW? 7.1 and 7.2 Apply Pythagorean Theorem and Use the Converse of Pythagorean Theorem · Find unknown leg or hypotenuse 1. Find the length of the hypotenuse of the right triangle. Trigonometry: 7.5 and 7.6 · What are the ratios for sine, cosine, and tangent? (Hint: Remember SohCahToa) · How can you find the sine, cosine, or tangent of a given angle? 1. Find sin B, cos B, and tan B. Write each answer as a fraction and as a decimal rounded to four places. · How can you use sine, cosine, and tangent to find the values of missing lengths of a triangle? 1. Basketball You walk from one corner of a basketball court to the opposite corner. The court is 94 feet long and your diagonal path creates a 62° angle from the baseline. Use a trigonometric ratio to calculate the distance you walk. 2. Roller Coaster You are at the top of a roller coaster 100 feet above the ground. The angle of depression is 44°. About how far do you ride down the hill? 3. Railroad A railroad crossing arm that is 20 feet long is stuck with an angle of elevation of 35° Find the lengths x and y 4. Lighthouse Find the height h of the lighthouse to the nearest foot. 7.7 Solving a Right Triangle: - What does it mean to “solve a right triangle” · What information must we know to solve a triangle? · What are the inverse trigonometric functions? · How can we find the measure of a given angle given the sine, cosine and tangent of that angle? Let A and B be acute angles in two right triangles. Use a calculator to approximate the measures of A and B to the nearest tenth of a degree. 1. sin A = 0.76 2. cos B = 0.17 · How can we use inverse trigonometric ratios to find the missing angles of a triangle? 1. In Example 1 solve the right triangle: 2. Model Train You are building a track for a model train. You want the track to incline from the first level to the second level, 4 inches higher, in 96 inches. Is the angle of elevation less than 3°? 3. Solve the right triangle. Round decimal answers to the nearest tenth. 4. Solve the right triangle. (find EVERYTHING!) Round answers to the nearest tenth. P 20 R 14 Q