## Plane and Spherical Trigonometry: An Elementary Text-book |

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### Other editions - View all

Plane and Spherical Trigonometry; An Elementary Text-Book Charles Hamilton Ashton,Walter Randall Marsh No preview available - 2019 |

### Common terms and phrases

acute angle of elevation apply balloon bank becomes called centre changes circle contain convenient corresponding cosine definitions determined difference equal equation EXAMPLE EXERCISE expressed figure Find the height Find the remaining finds the angle foot formulas functions give given greater Hence hold horizontal incline included increase length less logarithms magnitude manner measure method negative NOTE objects observer obtained opposite perpendicular plane pole positive positive direction possible problems proof Prove quadrant radius relations represent right angle right triangle seen shown sides similar sin a sin sin x sine sinº solution sphere spherical triangle stands straight student subtends tangent terminal lines theorem third tions tower triangle ABC trigonometric values vertical walks

### Popular passages

Page 122 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.

Page 91 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.

Page 99 - 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 1 - COR. 2. Two right triangles are similar if an acute angle of the one is equal to an acute angle of the other.

Page 90 - 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 109 - ... 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 20 - The angle of elevation of the top of a tower from a point P on the ground is 60°.

Page 56 - To find the sine and cosine of the sum and difference of two angles in terms of the sines and cosines of the angles themselves.

Page 112 - 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 112 - 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.