Plane and Spherical TrigonometryGinn, 1890 - 245 Seiten |
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Seite 6
... angle of elevation of the sun at the time of observation was found to be 0.82 . How high is a tower , if the length of its horizontal shadow at the same time is 174.3 yards ? § 2. REPRESENTATION OF FUNCTIONS BY LINES . The functions 6 ...
... angle of elevation of the sun at the time of observation was found to be 0.82 . How high is a tower , if the length of its horizontal shadow at the same time is 174.3 yards ? § 2. REPRESENTATION OF FUNCTIONS BY LINES . The functions 6 ...
Seite 22
... angle is twice the other . 59. In a right triangle given c , and AnB ; find a and b . 60. In a right triangle the difference between the hypote- nuse and the greater leg is equal ... angle of elevation of the sun when 223 22 TRIGONOMETRY .
... angle is twice the other . 59. In a right triangle given c , and AnB ; find a and b . 60. In a right triangle the difference between the hypote- nuse and the greater leg is equal ... angle of elevation of the sun when 223 22 TRIGONOMETRY .
Seite 23
... angle of elevation of the sun is 4 ° ? Find the height of the tree when b = 80 , A = 50 ° . 67. What is the angle of elevation of an inclined plane if it rises 1 foot in a horizontal distance of 40 feet ? 68. A ship is sailing due north ...
... angle of elevation of the sun is 4 ° ? Find the height of the tree when b = 80 , A = 50 ° . 67. What is the angle of elevation of an inclined plane if it rises 1 foot in a horizontal distance of 40 feet ? 68. A ship is sailing due north ...
Seite 70
... be 15 ° 13 ′ 15 ′′ . The angles of elevation of C viewed from A and B are 21 ° 9′18 ′′ and 23 ° 15 ' 34 " respectively . Find the distance from A to B. MISCELLANEOUS PROBLEMS . [ Selected by permission from " Problems 70 TRIGONOMETRY .
... be 15 ° 13 ′ 15 ′′ . The angles of elevation of C viewed from A and B are 21 ° 9′18 ′′ and 23 ° 15 ' 34 " respectively . Find the distance from A to B. MISCELLANEOUS PROBLEMS . [ Selected by permission from " Problems 70 TRIGONOMETRY .
Seite 71
... angle which a line drawn from the object to the point of observa- tion makes with the plane . If the object observed be situated above the horizontal plane ( that is , if it is farther from the earth's centre than ... angle of elevation of a.
... angle which a line drawn from the object to the point of observa- tion makes with the plane . If the object observed be situated above the horizontal plane ( that is , if it is farther from the earth's centre than ... angle of elevation of a.
Häufige Begriffe und Wortgruppen
ABC Fig absolute value acute angle altitude angle of depression angle of elevation azimuth celestial sphere centre circle of latitude colog computed cos² cosb cosc cosecant cosine cosp cosx cosy cotangent cotx csc B csc denote ecliptic equal equation equinoctial EXAMPLE EXERCISE feet find the angles Find the area Find the distance Find the height Find the value Given Hence horizontal plane hour angle hypotenuse included angle isosceles Law of Sines Leaving latitude log csc logarithms longitude meridian miles moving radius Napier's Rules negative oblique observer obtain perpendicular pole positive ratios regular polygon right ascension right spherical triangle right triangle secant ship sails sin B sin sin² siny solution solve the triangle spherical triangle star subtended tan² tanc tangent tower Trigonometry unit circle vertical whence
Beliebte Passagen
Seite 51 - The sides of a triangle are proportional to the sines of the opposite angles.
Seite 109 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Seite 52 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.
Seite 53 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Seite 142 - PZ, it follows that the altitude of the elevated pole is equal to the latitude of the place of observation. The triangle ZPM then (however much it may vary in shape for different positions of the star M), always contains the following five magnitudes : PZ= co-latitude of observer = 90°...
Seite 20 - Geometry that 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...
Seite 100 - Assuming the formula for the sine of the sum of two angles in terms of the sines and cosines of the separate angles, find (i.) sin 75° ; (ii.) sin 3 A in terms of sin A.
Seite 52 - The square of any side of a triangle is equal to the sum of the squares of the other two sides, diminished by twice the product of the sides and the cosine of the included angle.
Seite 70 - W., and after the ship had sailed 18 miles S. 67° 30' W. it bore N. 11° 15' E. Find its distance from each position of the ship. 2. Two objects, A and B, were observed from a ship to be at the same instant in a line bearing N. 15° E. The ship then sailed northwest 5 miles, when it was found that A bore due east and B bore northeast.
Seite 23 - From the top of a hill the angles of depression of two objects situated in the...