G.T. 7: state and apply the relationships that exist when the altitude is drawn to the hypotenuse of a right triangle. Understand and use the geometric mean to solve for missing parts of triangles. 8-1 Similarity in Right Triangles Theorem 8-1-1: The three altitudes in a right triangle will create three similar triangles http://www.mathwarehouse.com/geometry/similar/triangles/geometric-mean.php Geometric Mean: Find the geometric mean of each pair of numbers. If necessary, give the answer in simplest radical form. 1. and 8 2. 10 and 30 3. 8 and 9 x c a h b y ~ h y b ~ x h a orollary 8-1-2: b h a orollary 8-1-3: y c x
Find x, y, and z. 3 y x 9 z surveyor positions himself so that his line of sight to the top of a cliff and his line of sight to the bottom form a right angle as shown. If the man is 5.5 feet tall and is 28 feet away from the cliff, what is the height of the cliff to the nearest foot? n 8-inch long altitude of a right triangle divides the hypotenuse into two segments. One segment is 4 times as long as the other. What are the lengths of the segments of the hypotenuse? Prove the following. If the altitude to the hypotenuse of a right triangle bisects the hypotenuse, then the triangle is right triangle.
G.T.10: Use trigonometric ratios and the Pythagorean Theorem to solve real-world and mathematical problems involving right triangles. 8-2 Trigonometric Ratios Trigonometric ratio: efinition Symbols iagram Sine: osine: a c b Tangent: Write each trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. 7 24 25 1. 2. 3. Using a special right triangle to write the given trigonometric ratios. 4. 5. 6.
Use your calculator to find each trigonometric ratio. Round to the nearest hundredth. 7. 8. 9. Find each length. Round to the nearest hundredth. 10. F 11. ST 51 S F 17m E T 42 9.5 in U 12. 13. JL J 12 ft 18 K 27 13.6 cm L contractor is building a wheelchair ramp for a doorway that is 1.2 feet above the ground. To meet guidelines, the ramp will make an angle of 4.8 with the ground. To the nearest hundredth of a foot, what is the length of the ramp?
8-3 Solving Right Triangles Use the given trigonometric ratio to determine which angle of the triangle is. 1. 1 2. 30.6 m 14.4 m 2 27 m Inverse Trigonometric Function Trig Ratio Inverse If, then 30 2 If, then 1 60 If, then Use your calculator to find each angle measure to the nearest degree. 3. 4. 5. Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. 6. 14 E 7. X F 58 4.1 m Z 3.5 m Y EF = m = m F = XZ = m X = m Y =
8. X 9. Y 12 18 X 17 Z Y 15 Z XZ = m X = m Z = YX = m X = m Z = 10. The coordinates of the vertices of are and Find the side lengths to the nearest hundredth and the angle measures to the nearest degree. 11. aldwin Street in unedin, New Zealand, is the steepest street in the world. It has a grade of 38%. To the nearest degree, what angle does aldwin St. make with a horizontal line?
G.T.10: Use trigonometric ratios and the Pythagorean Theorem to solve real-world and mathematical problems involving right triangles. 8-4 ngles of Elevation and epression ngle of elevation: ngle of depression: Use the diagram to classify each angle as an angle of elevation or an angle of depression. 1. 2. 3. 4. 4 2 3 1 n air traffic controller at an airport sights a plane at an angle of elevation of. The pilot reports that the plane s altitude is 3500 feet. What is the horizontal distance between the plane and the airport?
forest ranger in a 90-foot observation tower sees a fire. The angle of depression to the fire is. What is the horizontal distance between the tower and the fire? Round to the nearest foot. pilot flying at an altitude of 12,000 ft sights two airports directly in front of him. The angle of depression to one airport is, and the angle of depression to the second airport is. What is the distance between the two airports? Round to the nearest foot. Plane irport irport skyscraper stands between two school buildings. The two schools are 10 miles apart. From school, the angle of elevation to the top of the skyscraper is. From school, the angle of elevation is. What is the height of the skyscraper to the nearest foot?