Geometry Warm Up Right Triangles Day 8 Date

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1 Geometry Warm Up Right Triangles Day 8 Name Date Questions 1 4: Use the following diagram. Round decimals to the nearest tenth. P r q Q p R 1. If PR = 12 and m R = 19, find p. 2. If m P = 58 and r = 5, find p. 3. If m P = 60 and p = 9, find q. 4. If r = 8 and p = 12, find q. 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.

2 Draw picture and apply word problem 1. A 5 foot board rests under a doorknob and the base of the board is 3.5 feet away from the bottom of the door. Approximately how high above the ground is the doorknob? Tell whether the given sides create a triangle. If so, is the triangle, acute, right or obtuse? Can segments with lengths of 6.1 inches, 9.4 inches, and 11.3 inches form a triangle? If so, would the triangle be acute, right, or obtuse? Recognize and know how to find common Pythagorean Triples 1. Use a Pythagorean triple to find the unknown side length of the right triangle. 7.3 Use Similar Right Triangles What is the altitude of a right triangle? Know how to write similarity statement for the three right triangles created by the altitude of a right triangle. 1. Identify the similar triangles in the diagram.

3 Geometric Mean (Altitude) Theorem 1. Find the value of x. Write your answer in simplest radical form. Geometric Mean (Leg) Theorem 1. Find the value of y. Write your answer in simplest radical form. 7.4 Recognize and Use Special Right Triangles What is the ratio of the sides and hypotenues for a 45, 45, 90 degree triangle? 1. Find the value of x. What is the ratio of the sides and hypotenuse for a 30, degree triangle? 1. Find the value of x. 2. A car is turned off while the windshield wipers are moving. The 24 inch wipers stop, making a 60 angle with the bottom of the windshield. How far from the bottom of the windshield are the ends of the wipers?

4 Note: How to find area of a triangle Draw a square with diagonals: Draw a rectangle with diagonals: Notice in the shape above, the acute angles are not 45 degrees each as the legs are not all the same length. Equilateral Triangle (altitude): Isosceles triangle (altitude): Notice that when we draw the altitude of an equilateral triangle, the base is separated into two equal pieces. 1. Find the area of the isosceles triangle with side lengths 16 meters, 17 meters, and 17 meters. Trigonometry: 7.5 and 7.6 What are the ratios for sine, cosine, and tangent? (Hint: Remember SohCahToa)

5 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.

6 7.7 Solving 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 = cos B = 0.17 How can we use inverse trigonometric ratios to find the missing angles of a triangle? 1. In Example 1, use a calculator and an inverse tangent to approximate m C to the nearest tenth of a degree. 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.