ENGTRIG: LECTURE # 4.2 Spherical Trigonometry Spherical Trigonometry Engr. Christian Pangilinan Areas of a Spherical Triangle A= π R2 E 180o E R E = A + B + C − 180o Where: spherical excess radius of the sphere Spherical Triangles Part of the surface of the sphere bounded by three arcs of three great circles Right Spherical Triangle – a spherical triangle containing at least one right angle If the sides are known instead of the angles‚ then L’Huiller’s Formula can be used
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sides. Roots of quadratic equations If a* + bx + c -0‚ x = then -b! bz - 4ac 2a Trigonometric ratios opposite side sin 0 = Epotenuse cos 0 Opposite = adjacent side Typotentrse Adjacent tan0 = Area of triangle Area of n = |øt where á is the length of the base and l¿ is the perpendicular height Area of MBC = þø "inc c c) (- Area of LABC = .fs(s - a)(s - b)(s c whete a sin A s= a+b+ Sine rule .ittB = únC
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Find the width of the track.(7 m) The area of a circle inscribed in an equilateral triangle is 154 cm 2. Find the perimeter of the triangle.(72.7 cm) ASSIGNMENT: 2 1. What is the area of shaded region if ABCD is a square of side 14 cm?(Ans: 42 cm2) 2. If the perimeter of the shaded region is 132 cm‚ find the area of the shaded region. (Ans: 173.25 cm2) 3. In the given figure‚ ABC is a right angled triangle‚ B = 900‚ AB = 28 cm and BC = 21 cm. With AC as diameter a semicircle is drawn
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© cxcDirect Institute CSEC MATHEMATICS Past Paper Solution – May 2014 cxcDirect Institute © All rights reserved. No part of this document may be reproduced without the written consent of the Author cxcDirect Institute Email: admin@cxcDirect.org Website: www.cxcDirect.org All Help videos are free‚ and can be viewed from our website © cxcDirect Institute © cxcDirect Institute ** Please see the original past paper for the questions. Only the answers will be provided as per
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CSIT 575 – Programming Fundamentals for Computer Science Lab #2A Objectives To learn to code‚ compile and run a sequential program To learn how to obtain a program listing and output printout Planning Due: ________________________ Program Listing and output Due: ________________________ Assignment Plan and code a program to do the following. The Natural Oak and Pine Furniture Company has hired you to develop a payroll program to print out a pay report for one employee. (Later‚ the program
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–3– M12/5/MATSD/SP1/ENG/TZ1/XX Maximum marks will be given for correct answers. Where an answer is incorrect‚ some marks may be given for a correct method‚ provided this is shown by written working. Write your answers in the answer IGCSE Revision 3 boxes provided. Solutions found from a graphic display calculator should be supported by suitable working‚ 1. 1. The following six integers are arranged from smallest to largest 1 ‚ x ‚ 3 ‚ y ‚ 14 ‚ z The mode is 1 ‚ the median is
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Assignments in Mathematics Class IX (Term 2) 8. QUADRILATERALS IMPORTANT TERMS‚ DEFINITIONS AND RESULTS l l Sum of the angles of a quadrilateral is 360°. A diagonal of a parallelogram divides it into two congruent triangles. In a parallelogram‚ (i) opposite sides are equal (ii) opposite angles are equal (iii) diagonals bisect each other A quadrilateral is a parallelogram‚ if (i) opposite sides are equal or (ii) opposite angles are equal or (iii) diagonals bisect each other or (iv) a pair of
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proved what‚ as the group wanted to keep their findings secret. Unfortunately‚ this vow of secrecy prevented an important mathematical idea from being made public. The Pythagoreans had discovered irrational numbers! If we take an isosceles right triangle with legs of measure 1‚ the hypotenuse will measure sqrt 2. But this number cannot be expressed as a length that can be measured with a ruler divided into fractional parts‚ and that deeply disturbed the Pythagoreans‚ who believed that "All is number
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symbols is as follows: Noun (black equilateral triangle) Article (small blue equilateral triangle) Adjective (medium dark blue equilateral triangle) Verb (red circle) Preposition (green crescent) Adverb (small orange circle) Pronoun (purple isosceles triangle) Conjunction (small pink rectangle) Interjection (golden keyhole) NOUN FAMILY Noun - a large black equilateral triangle Impressionistic Lesson:
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The materials I chose to use to build my three structures are toothpicks and small marshmallows. I chose these materials because I thought it would be fun to use with young children. It’s an activity that’s not messy just a little sticky and they can enjoy a sweet treat while working. The toothpicks and marshmallows are both small promoting help with fine motor development. The limit to only two types of materials to work with isn’t to over whelming. Also engaging their ability to think of different
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