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Plane and Spherical Trigonometry; An Elementary Text-Book
Charles Hamilton Ashton,Walter Randall Marsh
No preview available - 2019
1+tan ABē acute angle angle of depression angle of elevation angle XOA angles less axes circular measure congruent angles cosē cosēx cosecant cosine cotē cotangent cscē decrease indefinitely determined equal EXAMPLE EXERCISE expressed Find the distance Find the height Find the remaining finds the angle fourth quadrant func Functions of 45 given angle Hence horizontal hypotenuse less than 90 Let the student logarithms magnitude negative obtained obtuse perpendicular plane polar triangle positive direction proj Prove quadrant radius ratios represent right angle right triangle secē secant second quadrant signs sin a sin sin x sinē solution Solve the equation spherical triangle SPHERICAL TRIGONOMETRY subtends tanē tangent terminal line theorem third quadrant tions tower triangle ABC trigonometric functions values vertex vertical X-axis zero
Page 120 - I. The sine of the middle part is equal to the product of the tangents of the adjacent parts.
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.