Plane and Spherical Trigonometry: An Elementary Text-book
Scribner's, 1902 - Trigonometry - 157 pages
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Plane and Spherical Trigonometry; An Elementary Text-Book
Charles Hamilton Ashton,Walter Randall Marsh
No preview available - 2019
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acute angle of elevation apply approaches axes becomes called changes circle considered convenient cosē cosine cotangent curve decrease definitions determined difference distance draw drawn equal equation EXAMPLE EXERCISE expressed figure Find Find the remaining foot formulas functions give given greater height Hence hold horizontal increase length less logarithms magnitude manner measure method necessary negative NOTE objects observer obtained opposite origin perpendicular plane pole positive direction possible problems proj projection Prove quadrant radius ratios relations replace represent right angle right triangle secant seen shown sides similar sin a sin sinē sine solution Solve spherical triangle stands subtends tanē tangent terminal line third tions tower trigonometric values vertical
Page 120 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
Page 97 - Two sides of a triangle, and the angle opposite one of them, being given, to describe the triangle. Let A and B be the given sides, and C the given angle.
Page xiii - COR. 2. Two right triangles are similar if an acute angle of the one is equal to an acute angle of the other.
Page 88 - 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.
Page 107 - ... 12. Looking out of a window with his eye at the height of 15 ft. above the roadway, an observer finds that the angle of elevation of the top of a telegraph post is 17° 18' 35", and that the angle of depression of the foot of the post is 8° 32
Page 18 - The angle of elevation of the top of a tower from a point P on the ground is 60°.
Page 110 - The angle of elevation of a tower at a distance of 20 yd. from its foot is three times as great as the angle of elevation 100 yd.
Page 110 - Find the trigonometric functions of 48°. [HINT : 48° = 30° + 18°.] 12. Two parallel chords of a circle lying on the same side of the centre of a circle subtend angles of 72° and 144° at the centre. Show that the distance between the chords is equal to half the radius of the circle, (a) using tables, (6) not using tables.
Page 88 - 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.
Page 87 - Law of Sines - In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B...