Right Triangles and Trigonometry 8 2 Special Right

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Right Triangles and Trigonometry 8. 2 Special Right Triangles

Right Triangles and Trigonometry 8. 2 Special Right Triangles

Bell Work 1. What is the length of the hypotenuse of ∆RST? Do the

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.

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

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

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: √

45 -45 -90 TRIANGLES 45◦ s√ 2 s 45◦ s Ratio: 1: 1: √ 2 leg: hypotenuse

Example 1 Solve for the variables:

Example 1 Solve for the variables:

Example 2 A square has a diagonal of 15 cm. What is the length

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:

Example 3 Solve for the variables:

30 -60 -90 TRIANGLES 60◦ s 2 s 30◦ s√ 3 Ratio: 1: 1√

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 4 Solve for the variables.

Example 5 The frame for a garage roof is shown below. How long is

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

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 7 Solve for the variables: a = 18

Example 8 Solve for the variables: h =15

Example 8 Solve for the variables: h =15

Example 9 The side lengths of a triangle are given. Determine if the triangle

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

Homework Geometry Honors Pages 503 -505, #8 -30 even, 34, 35, 38, 39 Geometry Pages 528 -530, #8 -22 even