# Special Right Triangles - Geometry Writing Assignment...

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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° ; 20/2 = 10 = x a² + b² = c² (10)² + b² = (20)² 100 + b² = 400 √300 = b = 10√3 x = 10 and y = 10√3 2. Find the value of x and y. o 60 y Y: 60°, 30°, 90° c: 30; a: 30/2 = 15 = x P: 45°, 45°, 90° x = 15; b = 15 G: 60°, 30°, 90° a: 15; c: 15 x 2 = 30 y = 30 x = 15 and 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? 60°, 30°, 90° base = 4; hypotenuse = 4 * 2 = 8 a² + b² = c² ; (4)² + b² = (8)² ; 16 + b² = 64 ; b² = 48 b = √48 = 4√3 the top of the ladder is (4√3) m (approximately 6.93 m) above the ground 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 (18√3)/2 = 9√3 9√3 * 12 perimeter is 108√3 5. Find the value of x. 45°, 45°, 90° a = b, a = 45, b = 45 c = 45√2 x = 45√2 6. Find the value of x and y. left side: 45°, 45°, 90°: c: 8; a = b = 4√2 right side: 60°, 30°, 90°: a: 4√2; b: 8√6; c: 4√2 x 2 = 8√2; c = x = 8√2 b = y = 8√6 7. Find the value of x and y. 45°, 45°, 90° a = 3√2 x √2 c = 3√4 45°, 45°, 90° c = 3√2; a = b = 3/√2 o o o 8. the length of the leg of a 45 – 45 – 90 triangle with a hypotenuse length of 15 inches. x =Determine 3/√2 y = 3√4 45°, 45°, 90° c = 15in a = b = 15√2/√2 both legs are (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. since it is an equilateral triangle, all of the sides are equal. so the other two sides of the triangle would be the same as the altitude length. the length of any side of the triangle is 36 ft 10. Find x, y and z. left side: 30°, 60°, 90° b = 12; a = 4√3; c = 4√3 x 2 = 8√3 a = y = 4√3; c = z = 8√3 right side: 45°, 45°, 90° c = 12; a = b = 12√2 = 6√2 a = b = x = 6√2 x = 6√2 y = 4√3 z = 8√3 ...
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