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CW#70: 30-60-90 Special Right Triangles Geometry TEACHER NOTES CRS Objective PPF 601 – Apply properties of 30-60-90, 45-45-90, similar, and congruent triangles 8.14 Describe the relationship between sides of a 30-60-90 triangle , 9.10 Find the missing side length in a 30-60-90 triangle New Stuff: Example 1: Draw a 30-60-90 triangle. Label the side opposite the 30 degree angle 1 and label the hypotenuse 2. Solve for the missing leg. Example 2: Draw a 30-60-90 triangle. Label the side opposite the 30 degree angle 2 and label the hypotenuse 4. Solve for the missing leg. What is the ratio of the short leg to the long leg to the hypotenuse? What is the ratio of the short leg to the long leg to the hypotenuse? Essential Question: Is there a relationship between all three sides in a 30-60-90 triangle? In a 30-60-90 triangle, the hypotenuse is __________ as long as the short leg, and the long leg is __________ times as long as the short leg. Picture: Formulas: *Stress that the short leg is always opposite the 30 degree angle, and the long leg is opposite the 60 degree angle (relate this to the hypotenuse always being opposite the 90 degree angle). *Only the short leg is related to the hypotenuse and the long leg – there is NO way to get from the hypotenuse to the long leg or vice-versa. PUSH IT TO THE LIMIT. CW#70: 30-60-90 Special Right Triangles Geometry CLASSROOM COPY - DO NO WRITE ON THIS!!!! CRS Objective PPF 601 – Apply properties of 30-60-90, 45-45-90, similar, and congruent triangles 8.14 Describe the relationship between sides of a 30-60-90 triangle , 9.10 Find the missing side length in a 30-60-90 triangle Quick Review: 1) Find the missing side: 2) A 16 foot ladder rests against the side of the house, and the base of the ladder is 4 feet away. Approximately how high above the ground is the top of the ladder? What did you use to solve for the missing side? What did you use to solve for the missing side? NEW STUFF: Example 1) Find x and y. Example 2) Find x and y. Example 3) Find x and y. Example 4) The altitude of an equilateral triangle is 10 centimeters. Find the perimeter of the triangle. Round to the nearest tenth. Find the value of each variable. Write your answers in simplest radical form. 1) 2) 3) 4) 5) 6) PUSH IT TO THE LIMIT. 7) Use the figure at the right to complete the table below. ⁰ 8) In the diagram below, which side length is the longest? A. a B. b C. c D. d 10) The altitude of an equilateral triangle is 12 centimeters. Find the perimeter of the triangle. Round to the nearest tenth. ⁰ 9) A 24 foot long bleacher stand has a base angle 30. How high above the ground is the last row of seating? ⁰ 11) The perimeter of a rectangle is 32 feet. The length is three times as long as the width. Find the length of the diagonal. Round to the nearest tenth. 12) Each figure below is a 30°-60°-90° triangle. Find 13) The perimeter of an equilateral triangle is 45 the value of x. Round to the nearest tenth. meters. Find the length of an altitude. Round to the nearest tenth. 14) A symmetrical canyon is 4850 feet deep. A a. Find the distance across the canyon river runs through the canyon at its deepest point. The angle of depression from each side of the canyon to the river is 60°. Round to the nearest tenth. b. Find the length of the canyon wall from the edge to the river PUSH IT TO THE LIMIT.