Writing Assignment Special Right Triangles - Geometry...

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Trigonometry
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Chapter 1 / Exercise 19
Trigonometry
Larson
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Unformatted text preview: Geometry Writing Assignment: Special Right Triangles Each problem is worth 5 points. Total points: 50 Solve the problems pertaining to special right triangles. Leave all answers as reduced radicals. 1. Find the value of x and y. 180° - (90° + 30°) = 180° - 120° = 60° 30°-60°-90° Right Triangle "If you know the hypotenuse, divide by 2 to get the shortest leg and the use that value to find the longer leg." 20/2 = 10 x = 10; y = 10√3 L² + L² = H² (10)² + L² = (20)² 100 + L² = 400 (100 - 100) + L² = (400 - 100) L² = √300 = L = 10√3 2. Find the value of x and y. o 60 y Yellow Triangle: 60°, 30°, 90° Hypotenuse: 30; Shortest Leg: 30/2 = 15 Green Triangle: 45°, 45°, 90° x = 15; L2 = 15 Green Triangle: 60°, 30°, 90° Shortest Leg: 15; Hypotenuse: 15 x 2 = 30 y = 30 x = 15; y = 30 o 3. A ladder leaning against a wall makes a 60 angle with the ground. The base of the ladder is 4 m from the building. How high above the ground is the top of the ladder? Triangle: 60°, 30°, 90°; Base = 4; Hypotenuse = 4 * 2 = 8; ² L² + L² = H²; (4)² + L² = (8)²; 16 + L² = 64; (16 - 16) + L² = (64 - 16); L² = 48 L = √48 = 4√3 4. A regular hexagon is composed of 12 congruent 30 o -60 o -90 o triangles. If the length of the hypotenuse of one of those triangles is 18 3 , find the perimeter of the hexagon. Hypotenuse: 18√3; Shortest Leg: (18√3)/2 = 9√3 Perimeter: 9√3 * 12 Perimeter: 108√3 5. Find the value of x. Triangle: 45°, 45°, 90° L1 = 45, L2 = 45 Hypotenuse = 45√2 x = 45√2 6. Find the value of x and y. Triangle 1 (45°, 45°, 90°): Hypotenuse: 8; Legs = 4√2 Triangle 2 (60°, 30°, 90°): Shortest Leg: 4√2; Hypotenuse: 4√2 x 2 = 8√2; Longest Leg: 8√6 x = 8√2; y = 8√6 7. Find the value of x and y. Triangle 1 = 45°, 45°, 90° Leg = 3√2 x √2 Hypotenuse = 3√4 Triangle 3 = 45°, 45°, 90° Hypotenuse = 3√2; Legs = 3/√2 x = 3/√2; y = 3√4 o o o 8. Determine the length of the leg of a 45 – 45 – 90 triangle with a hypotenuse length of 15 inches. Triangle: 45°, 45°, 90° Hypotenuse = 15in Legs = 15√2/√2 The legs are both 15√2/√2 inches long. 9. An equilateral triangle has an altitude length of 36 feet. Determine the length of a side of the triangle. In an equilateral triangle, all sides are equal. As a result, the other two sides of the triangle would each be equal to the altitude length, The length of a side of the triangle is 36ft. 10. Find x, y and z. Triangle 1 = 30°, 60°, 90° Longest Leg = 12; Shortest Leg = 12/√3 = 4√3; Hypotenuse = 4√3 x 2 = 8√3 y = 4√3; z = 8√3 Triangle 2 = 45°, 45°, 90° Hypotenuse = 12; Legs = 12√2 = 6√2 x = 6√2 x = 6√2; y = 4√3; z = 8√3 ...
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