## 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

ABē ACē acute angle of depression angle of elevation angle opposite balloon CDē circular measure congruent angles cosē cosecant cotē cotangent cscē decrease indefinitely determined equal EXAMPLE EXERCISE expressed Find the distance Find the height Find the remaining Find the three finds the angle foot Functions of 45 given angle Hence hypotenuse included angle length less than 90 Let the student log sin logarithms magnitude negative obtained obtuse perpendicular polar triangle pole positive direction proj Prove quadrant quadrantal triangle radius represent right angle right spherical triangle right triangle rotation secē secant sin a sin sinē sine solution spherical angle spherical triangle SPHERICAL TRIGONOMETRY tanē tangent terminal line theorem three angles three sides tions tower trigonometric functions values vertex vertical X-axis

### 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.