10. Determine the area of an ellipse, the transverse axis being 7.38, and the conjugate 4.71.

11. Compute the number of cubic feet in a cone, whose base is 356 inches in diameter, and whose height is 98 inches.

12. What is the weight of an ivory ball 12 inches in diameter, at the rate of 1820 ounces (Av.) to the cubic foot?

EXERCISES IN CHAPTER VI, PROBLEM I.

1. What are the log. sines of 24°, of 68°, of 35° 32', and of 84° 15'?

2. What is the log. tangent of 32° 12', and that of 48° 40'?

3. What is the log. cosine of 18° 24', and the log. secant of 50° 8'?

EXERCISES IN CHAPTER VI, PROBLEM II.

Find the log. sine of 22° 48′ 54", the log. tangent of 63° 25′ 16′′, the log. secant of 38° 14′ 5", and the log. cosine of 76° 0' 48".

EXERCISES IN CHAPTER VI, PROBLEM V.

What are the log. sines of 104° 18′, 126° 12′ 24′′, and 164° 54' 48" ?

EXERCISES IN CHAPTER VI, PROBLEM VII.

What angles correspond to log. sine 9.520271, log. tangent 10.407574, and log. secant 10.566325 ?

2. Find the numbers of degrees and minutes corresponding to log. sine 9.284776, log. tan 10-550548, and log. secant 11.132496.

3. What are the angles answering to log. cosine 9.995555, to log. cotan 10.508800, and to log. cosecant 10.030568?

EXERCISES IN CHAPTER VII, PROBLEM I.

1. The acute angle at the base of a right-angled triangle is 1830 what is that at the vertex ?

2. The acute angle at the vertex being 84° 13', what is that at the base?

3. If the one acute angle contain 28° 44′ 55′′, how degrees are in the other?

many

EXERCISES IN CHAPTER VII, PROBLEM II.

1. Hyp. = 5438. Acute angle at base = 35°. required.

=

Perp.

2. Hyp. 249. Acute angle at vertex = 43° 25'. Base required.

=

3. Hyp. 1000.

are the legs?

=

One acute angle = 36° 16'. What

4. Hyp. 04. Angle at base = 43° 40'. Sides required.

5. Hyp.8.2958. Acute angle at vertex = 54° 23'. Perp. required.

EXERCISES IN CHAPTER VII, PROBLEM III.

1. Base 845. Adjacent acute angle = 28° 25'. Hyp. required.

2. Perp. required.

=

Vertical angle 59° 12'. Hyp.

=

3. Base 4.843. Vertical angle = 7°. Hyp. required. 4. Compute, by Trigonometry, the diagonal of a square whose side is 749.

=

5. Perp. 583.26. Acute angle at base Hyp. required.

EXERCISES IN CHAPTER VII, PROBLEM IV.

14.04. Acute angle adjacent = 72° 48′. Perp.

2. Perp.3 ft. 4 in. Vertical angle = 22° 28'. Base

required.

3. Base

required.

= 384. Vertical angle = 48° 26′ 12′′.

=

4. Base 0.440,83. 38.2'. Perp. required.

EXERCISES IN CHAPTER VII, PROBLEM V.

=

=

1. Hyp. 123. Perp. 84. The angles are required. 2. Base-0.8. Perp. 1.2.

=

What are the angles?

3. The base of an isosceles triangle is 5, and each of its equal sides double the base. What is the vertical angle?

EXERCISES in CHAPTER VII, PROBLEM VI.

1. The legs being 2 and 3, 2. Base=3 yds. 1 ft. 6 in.

are the acute angles?

what are the acute angles? Perp. =5 yds. 9 in. What

3. What is the angle of inclination of a gradient rising at the rate of 1 in 28?

4. The legs being 0096 and 0192, what are the acute angles?

EXERCISES IN CHAPTER VII, PROBLEM VII.,

=

1. Hyp. 8 ft. 5 in. Base = 6 ft. 4 in. Perp. required.

2. Hyp. = 8125. Perp. 3125. Base required. 3. Hyp. 0.13167. Base = 02660. Perp. required.

=

EXERCISES IN CHAPTER VII, PROBLEM VIII.

=

=

1. Base 12.6. Perp. 1.33. Hyp. required. 2. Base 26. Perp. 128.7. Hyp. required. 3. Legs 0784 and 0377. Hyp. required.

PROMISCUOUS EXERCISES IN RIGHT-ANGLED TRIANGLES.

1. Hyp. 101. Perp. 99. Base required.

=

2. One of the equal sides of an isosceles triangle is 19-49, and the angle at the vertex 45°. What is the base? 3. Compute, by Trigonometry, the side of an equilateral triangle whose altitude is 100.

4. The three sides of a triangle are 193, 193, and 190. Taking the shortest side as the base, what is the altitude, and what are the angles at the base?

5. The largest of the pyramids of Egypt, being more correctly a frustum of a pyramid, is 480 feet high, and stands on a base 745 feet square, its summit being 32 feet

square. At what angle are the sides inclined to the horizon?

6. One of the acute angles of a right-angled triangle is four times the other. The shorter leg is 10. What is the

longer leg, and the hypothenuse?

EXERCISES IN CHAPTER VIII, PROBLEM I.

1. Given, the angles at the base 333° and 5910. Required the angle at the vertex.

2. A 84° 49'.

=

3. B 49° 10′ 53′′. <C=72° 57' 15". A is required.

4. The sum of the angles at the base of a triangle is 114° 483'. What is the angle at the vertex?

5. The angle at the vertex being 774°, what is the sum of the angles at the base?

EXERCISES IN CHAPTER VIII, PROBLEM II.

1. Given,

A = 49° 54', ≤B=72° 28', side a=769. Required side b.

2. The three angles of a triangle are respectively 54°, 69°, and 57°. The shortest side is 8.58 chains. What are the other two sides?

3. Two angles of a triangle are severally 39° 10′ and 104° 48'. The side opposite the former is 48 yds. 2 ft. What is the side opposite the latter?

4. What is the third side of the last-mentioned triangle?

EXERCISES IN CHAPTER VIII, PROBLEM III.

1. Side a=4.94. Side b=5.09.

<B=118°. A is

required.

2. Sides a and b = 5 and 6. A=541°. ZB is required, which is acute.

3. Sides a and b 0.3 and 0.4. A= 38° 43'. B

is required, which is obtuse.

4. Side a= = 548.3. Side b=499.4.

What is B?

ZA=76° 23'.

5. Side a=10. Side b=11. ZA=57° 4′. What is

ZB?

EXERCISES IN CHAPTER VIII, PROBLEM IV.

Compute the third side in each of the five triangles described in the Exercises under the preceding Problem.

EXERCISES IN CHAPTER VIII, PROBLEM V.

1. Sides, 4 and 5. Included angle, 66°. What are the other angles?

2. Sides, 8 and 9ğ. angles are required. 3. Sides, 2 and 23.

pute the other angles.

Vertical angle, 1810. The other

Included angle, 96° 20'. Com

EXERCISE IN CHAPTER VIII, PROBLEM VI.

Calculate the third side of each of the three triangles described in the preceding Exercises, under Problem v.

EXERCISES IN CHAPTER VIII, PROBLEM VII.

1. The three sides being 1636, 1524, and 1540, what are the three angles?

2. Sides, 11-46, 9.68, and 8.674. What are the angles?

EXERCISES IN CHAPTER IX.

NOTE. Instead of giving a new set of questions in this place, it has been thought better merely to give repetitions of those in Chapter IX, with the figures altered. Thus, of the following questions, the first is understood to be the same as Exercise 1 of that Chapter, substituting 12 degrees for 15, and 36 feet for 50.

4.

5.

6.

18 miles West... ..20 miles South......?

5... 21........201

.NNW, 12 miles.

?

?