Plane Trigonometry, for Colleges and Secondary SchoolsLongmans, Green, and Company, 1899 - 206 páginas |
Dentro del libro
Resultados 1-5 de 14
Página 17
... Tower and Notre Dame Cathedral is 71⁄2 in . What is the distance between those points , the map being drawn to a scale 1 : 20000 ? 8. Make the comparison of angles asked for in Exs . 8 , 9 , 10 , Art . 8 ; Exs . 11 , 12 , 13 , Art . 9 ...
... Tower and Notre Dame Cathedral is 71⁄2 in . What is the distance between those points , the map being drawn to a scale 1 : 20000 ? 8. Make the comparison of angles asked for in Exs . 8 , 9 , 10 , Art . 8 ; Exs . 11 , 12 , 13 , Art . 9 ...
Página 51
... tower , the angle of elevation of the top of the tower is observed to be 60 ° . Find the height of the tower . Let AB be the tower , and P the point of observa- tion . By the observations , B D O AP = 150 ft . , APB = 60 ° . - AB AP tan ...
... tower , the angle of elevation of the top of the tower is observed to be 60 ° . Find the height of the tower . Let AB be the tower , and P the point of observa- tion . By the observations , B D O AP = 150 ft . , APB = 60 ° . - AB AP tan ...
Página 52
... tower , and on a level with its base , the eleva- tion of the top of the tower is found to be 65 ° 40.5 ' . What is the height of the tower ? 5. From the top of a tower 120 ft . high the angle of depression of an object on a level with ...
... tower , and on a level with its base , the eleva- tion of the top of the tower is found to be 65 ° 40.5 ' . What is the height of the tower ? 5. From the top of a tower 120 ft . high the angle of depression of an object on a level with ...
Página 114
... tower at the extremities of the line are 32 ° and 58 ° , the height of the observer's eye being 5 ft . 7. Find the height of a tower on top of a hill , when a horizontal base line on a level with the foot of the hill and in the same ...
... tower at the extremities of the line are 32 ° and 58 ° , the height of the observer's eye being 5 ft . 7. Find the height of a tower on top of a hill , when a horizontal base line on a level with the foot of the hill and in the same ...
Página 115
... tower subtends an angle a at a point on the same level as the foot of the tower and , at a second point , h feet above the first , the depression of the foot of the tower is B. Show that the height of the tower is h tan a cot ß . 13 ...
... tower subtends an angle a at a point on the same level as the foot of the tower and , at a second point , h feet above the first , the depression of the foot of the tower is B. Show that the height of the tower is h tan a cot ß . 13 ...
Contenido
134 | |
135 | |
137 | |
138 | |
139 | |
146 | |
147 | |
149 | |
55 | |
61 | |
64 | |
67 | |
92 | |
98 | |
106 | |
110 | |
113 | |
115 | |
116 | |
117 | |
118 | |
119 | |
120 | |
121 | |
122 | |
123 | |
128 | |
129 | |
131 | |
151 | |
156 | |
157 | |
158 | |
159 | |
185 | |
1 | |
13 | |
39 | |
40 | |
49 | |
52 | |
54 | |
58 | |
60 | |
61 | |
74 | |
75 | |
83 | |
Otras ediciones - Ver todas
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'.