By Percival Frost Joseph Wolstenholme

This Elibron Classics e-book is a facsimile reprint of a 1863 version by means of Macmillan and Co., Cambridge - London.

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This Elibron Classics e-book is a facsimile reprint of a 1863 version through Macmillan and Co. , Cambridge - London.

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**Additional info for A Treatise on Solid Geometry**

**Example text**

673 The boat travels 454 ft in 2 min; its speed is 227 ft/min. 16 Find, to four decimal places, the values of the six trigonometric functions of each of the following angles: (a) 18Њ47Ј, (b) 32Њ13Ј, Ans. 67Њ, Ans. 8900 Ans. 4651 Ans. 24 Ans. 20 Find the base and altitude of an isosceles triangle whose vertical angle is 65Њ and whose equal sides are 415 cm. Ans. 90 in and the base angles are 54Њ28Ј. Find the equal sides and the altitude. Ans. 4 m. Find (a) the length of the chord subtended by a central angle of 110Њ40Ј and (b) the distance between two parallel chords on the same side of the center subtended by central angles 118Њ40Ј and 52Њ20Ј.

A) sin 30Њ ϩ tan 45Њ (b) cot 45Њ ϩ cos 60Њ (c) sin 30Њ cos 60Њ ϩ cos 30Њ sin 60Њ (d) sec 55Њ 38 CHAPTER 3 Trigonometric Functions of an Acute Angle (d) cos 30Њ cos 60Њ ϩ sin 30Њ sin 60Њ tan 60Њ Ϫ tan 30Њ (e) 1 ϩ tan 60Њ tan 30Њ csc 30Њ ϩ csc 60Њ ϩ csc 90Њ (f) sec 0Њ ϩ sec 30Њ ϩ sec 60Њ Ans. 21 (f) 1 Manual: 170 m; calculator: 171 m (manual answer differs because of rounding of table values). 55 ft Manual: 3730 m; calculator: 3732 (manual answer differs because of rounding of table values). 90 m A ladder with its foot in the street makes an angle of 30Њ with the street when its top rests on a building on one side of the street and makes an angle of 40Њ with the street when its top rests on a building on the other side of the street.

For the problems in this chapter, a manual solution and a calculator solution will be shown and an answer for each procedure will be indicated. In later chapters, an answer for each method will be indicated only when the two procedures produce different results. 30 CHAPTER 3 Trigonometric Functions of an Acute Angle The decision to use or not to use a calculator is a personal one for you to make. If you will not be able to use a calculator when you apply the procedures studied, then do not practice them using a calculator.