Right Triangles and Trigonometry 8 2 Special Right
- Slides: 17
Right Triangles and Trigonometry 8. 2 Special Right Triangles
Bell Work 1. What is the length of the hypotenuse of ∆RST? Do the side lengths of ∆RST form a Pythagorean triple? Explain. 2. Cassie’s computer monitor is in the shape of a rectangle. The screen on the monitor is 11. 5 in. high and 18. 5 in. wide. What is the length of the diagonal? Round to the nearest tenth of an inch. 3. A triangle has side lengths 9, 10, and 12. Is it acute, obtuse, or right? Explain.
Bell Work Answers 1. 15; Yes, because all three side lengths are whole numbers. 2. 21. 8 in. 3. Acute; 144<181 so the triangle is acute by Theorem 8 -4.
Learning Goal The student will understand how use the properties of special right triangles to find the lengths of the legs and hypotenuse given one measure.
Learning Scale 4: I can do all the requirements for the 3, prove the Pythagorean Theorem several ways and solve unique real world problems. 3. I can find the missing lengths of any side of a special right triangle using the ratios of 30 -60 -90 and 45 -45 -90 triangles and can simplify and rationalize radical expressions. 2: I can usually find the missing lengths of any side of a special right triangle using the ratios of 30 -60 -90 and 45 -45 -90 triangles. I have difficulty simplifying radicals. I understand the ratios but have difficulty identifying which portion of the ratios go with which side of the triangle. I can not rationalize the denominator of a radical expression. 1: With the help of the teacher, peers, notes, and online textbook, I can partially find the missing length of any side of a special right triangle, by using the ratios of 30 -60 -90 an 45 -45 -90 triangles. 0: I do not understand
45 -45 -90 TRIANGLES 45◦ s√ 2 s 45◦ s Ratio: 1: 1: √ 2 leg: hypotenuse
Example 1 Solve for the variables:
Example 2 A square has a diagonal of 15 cm. What is the length of a side? Express in simplest radical form. 15 cm x
Example 3 Solve for the variables:
30 -60 -90 TRIANGLES 60◦ s 2 s 30◦ s√ 3 Ratio: 1: 1√ 3: 2 short leg: long leg: hypotenuse
Example 4 Solve for the variables.
Example 5 The frame for a garage roof is shown below. How long is each side of the roof?
Example 6 An equilateral triangle has perimeter 120 in. What is the area of the triangle? Express your answer in simplest radical form. Each side is 40 in. 30 o 40 h= 60 o 20 b 20
Example 7 Solve for the variables: a = 18
Example 8 Solve for the variables: h =15
Example 9 The side lengths of a triangle are given. Determine if the triangle is a 45º-90º triangle, a 30º-60º-90º triangle, or neither. • 40, 50, 80 Neither • 6√ 2, 12 45º-90º • 31, 31√ 3, 62 30º-60º-90º
Homework Geometry Honors Pages 503 -505, #8 -30 even, 34, 35, 38, 39 Geometry Pages 528 -530, #8 -22 even
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