Elementary Text-book of TrigonometryBlackie & Son, 1884 - 176 páginas |
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Página 45
... Heights and Distances . One of the most important applications of trigonometry is the determination of the heights and distances of objects which cannot be actually measured . We shall consider a few APPLICATIONS OF RATIOS . 45.
... Heights and Distances . One of the most important applications of trigonometry is the determination of the heights and distances of objects which cannot be actually measured . We shall consider a few APPLICATIONS OF RATIOS . 45.
Página 46
... Height of an Accessible Object . Let AB be a vertical object , such as a tower or a church D 14 spire , of which the height B AB is required . From A , the foot of the object , let a convenient distance AC be measured on a level with A ...
... Height of an Accessible Object . Let AB be a vertical object , such as a tower or a church D 14 spire , of which the height B AB is required . From A , the foot of the object , let a convenient distance AC be measured on a level with A ...
Página 47
... height of the tree , given tan25 ° 37 ′ = ' 479 . Here therefore CA = 100 feet , tan ACB = tan 25 ° 37 ' = ' 479 ; AB , the height of the tree = 100 × 479 = 47.9 feet . Ex . 3. From the top of a cliff the angle of depression of a buoy ...
... height of the tree , given tan25 ° 37 ′ = ' 479 . Here therefore CA = 100 feet , tan ACB = tan 25 ° 37 ' = ' 479 ; AB , the height of the tree = 100 × 479 = 47.9 feet . Ex . 3. From the top of a cliff the angle of depression of a buoy ...
Página 48
... height AB . Also BC AC cosACB = a tanẞ × cosa , = which gives the distance BC . Ex . a = 100 feet , a = 30 ° , ß = 45 ° . AB , the height = 100 × sin30 ° × tan45 ° = 100 × × 1 = 50 feet . = BC , the distance = 100 x cos30 ° x tan45 ...
... height AB . Also BC AC cosACB = a tanẞ × cosa , = which gives the distance BC . Ex . a = 100 feet , a = 30 ° , ß = 45 ° . AB , the height = 100 × sin30 ° × tan45 ° = 100 × × 1 = 50 feet . = BC , the distance = 100 x cos30 ° x tan45 ...
Página 49
... height . = AB cota = a cota cota - cotß Ex . a = 30 ° , B = 45 ° , a = 60 feet . Height = 60 cot30 ° - cot45 ° = 60 ( Art . 16 ) tan60 ° - tan45 ° 60 60 ( √3 + 1 ) - √3-1 3-1 = 30 ( √3 + 1 ) = 81.96 feet . EXAMPLES IX . 1. From the ...
... height . = AB cota = a cota cota - cotß Ex . a = 30 ° , B = 45 ° , a = 60 feet . Height = 60 cot30 ° - cot45 ° = 60 ( Art . 16 ) tan60 ° - tan45 ° 60 60 ( √3 + 1 ) - √3-1 3-1 = 30 ( √3 + 1 ) = 81.96 feet . EXAMPLES IX . 1. From the ...
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Términos y frases comunes
angle AOB angle BAC angle increases angle less Article base centre circumference cloth boards common logarithm complement cos(A+B cos2A cos4A cosB cosC cose cosecA cosine cotA cotangent decimal places degree measure diameter distance equal equation Euclid EXAMPLES feet Find the angle Find the height find the number find the values flagstaff following angles formula given Hence hypotenuse inches log2 loga logarithms of numbers magnitude mantissa miles negative numbers number expressing number of degrees numerical value perpendicular positive Prove quadrant radian measure radii ratios of angles regular polygon respectively right angle right-angled triangle sec²A secA secant side BC Similarly sin(A sin(A+B sin2A sin2B sin3A sinB sine sine and cosine square root table of logarithms tan(A+B tan²A tanA tanB tangent tanß tower triangle ABC trigono trigonometrical ratios unit of angle yards
Pasajes populares
Página 90 - The logarithm of the product of two or more numbers is equal to the sum of the logarithms of the numbers. For, let m and n be two numbers, and x and y their logarithms. Then, by the definition of a logarithm, m — ax, and n = a".
Página 90 - ... the logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
Página 118 - In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...
Página 149 - Find the length of the side of a square whose area is equal to that of a rectangle the sides of which are 94 '28 and 6720 yards.
Página 89 - The logarithm of a number is the index of the power to which the base of the system must be raised to equal a given number.
Página 158 - The sides of a triangle are in arithmetical progression, and its area is to that of an equilateral triangle of the same perimeter as 3 : 5.