Plane Trigonometry, for Colleges and Secondary SchoolsLongmans, Green, and Company, 1899 - 206 páginas |
Dentro del libro
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Página 11
... respectively . EXAMPLES . 1. What is the ratio of each of the following lengths to an inch , viz . , 8 in . , 2 ft . , 3 ft . 6 in . , 1.5 yd . , 20 yd . , a yd . , b ft . , c in . ? 2. What is the ratio of each of the following lengths ...
... respectively . EXAMPLES . 1. What is the ratio of each of the following lengths to an inch , viz . , 8 in . , 2 ft . , 3 ft . 6 in . , 1.5 yd . , 20 yd . , a yd . , b ft . , c in . ? 2. What is the ratio of each of the following lengths ...
Página 20
... respectively . 5. Same as Ex . 2 , for a right - angled triangle whose hypotenuse is 60 ft . and base is 45 ft . 6. Same as Ex . 2 , for a right - angled triangle in which the base is 50 ft . and the angle opposite to the base is 40 ...
... respectively . 5. Same as Ex . 2 , for a right - angled triangle whose hypotenuse is 60 ft . and base is 45 ft . 6. Same as Ex . 2 , for a right - angled triangle in which the base is 50 ft . and the angle opposite to the base is 40 ...
Página 28
... respectively . Measure angle ACB with the pro- Measure BC directly in the figure . tractor . Method of computation . BC = VAC2 - AB2 = √576 – 64 = √ / 512 = 22.63 ft . FIG . 7 . AB 8 sin ACB = = .33333 , = AC 24 ... ACB 19 ° 28 ' 16 ...
... respectively . Measure angle ACB with the pro- Measure BC directly in the figure . tractor . Method of computation . BC = VAC2 - AB2 = √576 – 64 = √ / 512 = 22.63 ft . FIG . 7 . AB 8 sin ACB = = .33333 , = AC 24 ... ACB 19 ° 28 ' 16 ...
Página 30
... respectively proportional to 1 , √3 , 2. Hence , in order to produce the ratios of 30 ° , 60 ° , at a moment's notice , it is merely necessary to draw Fig . 12 , from which these ratios can be immediately read off . C. Ratios of 0 ...
... respectively proportional to 1 , √3 , 2. Hence , in order to produce the ratios of 30 ° , 60 ° , at a moment's notice , it is merely necessary to draw Fig . 12 , from which these ratios can be immediately read off . C. Ratios of 0 ...
Página 38
... is as follows : Construct a triangle QPR having two sides , PQ , PR , representing 10 ft . , 5 ft . , respectively , on some con- 38 venient scale , and shown in Fig . 14 . The graphical method គ ៖ Solution of a triangle.
... is as follows : Construct a triangle QPR having two sides , PQ , PR , representing 10 ft . , 5 ft . , respectively , on some con- 38 venient scale , and shown in Fig . 14 . The graphical method គ ៖ Solution of a triangle.
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Términos y frases comunes
A+B+C acute angle algebraic angle of elevation central angle CHAPTER circle circumscribing cologarithm column computation cos² cosec cotangent deduced denoted Derive draw equal equation EXAMPLES expression figures find log Find the angle Find the distance Find the height find the number formulas geometrical Given log graph Hence Hipparchus hypotenuse inverse trigonometric functions isosceles triangle law of sines length M₁ mantissa mantissa of log mathematics method negative NOTE number of degrees number of sides OP₁ perpendicular proj Prove radian measure radius regular polygon revolving right angles right-angled triangle sec² secant Show shown sin² sin³ sine and cosine Solve spherical trigonometry subtended tan-¹ tan² tangent terminal line theorems tower triangle ABC trigono trigonometric functions trigonometric ratios turning line whole number X₁
Pasajes populares
Página 100 - These formulas can be expressed in words : In any triangle, the square of any side is equal to the sum of the squares of the other two sides minus twice the product of these two sides multiplied by the cosine of their included angle.
Página 54 - The area of a triangle is equal to one-half the product of the base by the altitude ; therefore, if a and b denote the legs of a right triangle, and F the area, F = \ ab.
Página 122 - It follows that the ratio of the circumference of a circle to its diameter is the same for all circles.
Página 192 - The area of a regular polygon inscribed in a circle is a geometric mean between the areas of an inscribed and a circumscribed regular polygon of half the number of sides.
Página vii - ... facility other French books. In the Dictionary at the end, is given the meaning of every- word contained in the book. The explanatory words are placed at the end of the book, instead of at the foot of the page; by this method learners will derive considerable benefit.
Página 83 - P'M' = sin a, OP' = cos a, AT'" = tan a, JBT" = cot a, OT" = sec a, OT'" = cosec a, without reference to their signs : hence, we have, as before, the following relations : sin (180° — a) = sin a, cos (180° — a) — — cos a, tan (180° — a) = — tan a, cot (180° — a) = — cot a, sec (180° — a) = — sec a, cosec (180 — a) = cosec a, By a similar process, we may discuss the remaining arcs b question.
Página 5 - The characteristic of the logarithm of a number greater than 1 is a positive integer or zero, and is one less than the number of digits to the left of the decimal point.
Página 189 - Two observers on the same side of a balloon, and in the same vertical plane with it, are a mile apart, and find the angles of elevation to be 17° and 68° 25' respectively : what is its height ? [1836 feet.
Página 54 - Hence, the area of a triangle is equal to one-half the product of any two sides ' and the sine of their contained angle. EXAMPLES. 1. Find the area of the triangle in which two sides are 31 ft. and 23 ft. and their contained angle 67° 30'.