Plane and Spherical Trigonometry

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Ginn, 1890 - 245 Seiten

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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...

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