Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

C 53°.6', the Complement of A, may be found by the following Proportion, as in the laft Problem:

As the Sine of the Angle at A, 36°. 54,

[blocks in formation]

Is to the Perpendicular B C, 35.66,
So is the Sine of the Angle at C, 53°.6,

[blocks in formation]

To the Bafe A B, 47.5,

1.676705

.

Which may be measured by the general Rule, Prob. 19.

Prob. 21. In the right-angled Triangle ABC, rightangled at B, given the Hypothenufe AC 59.4, and the Angle at A 36°. 54, to find the Bafe A B, and the Perpendicu lar BC.

Conftruction. Draw a Bafe-Line at Pleasure, as before, and, from the Point A, fet off the given Angle 36°. 54 from the Line of Chords, by Prob. 8; draw the Hypothenuse A C to a convenient Length, and, from the diagonal Scale, by the general Rule, Prob. 19, take 59.4 in the Compaffes, and fet it from A to C; from the Point C let fall a Perpendicular to the Line A B, by Prob. 4, Cafe 2, and the Triangle is completed.

A

B

Here the right Angle, which is always known, is oppofite the given Hypothenufe; and the Angle at A is given, and oppofite the Perpendicular, one of the Parts required; which may be found by the following Proportion:

As the Radius, or Sine of the Angle at B,

Is to the Hypothenufe A C, 59.4,
So is the Sine of the Angle at A, 36°. 54',

To the Perpendicular B C, 35.66,

10.

1.773786 9.778455

1.552241

Which may be measured by the general Rule, Prob. 19.

[ocr errors]
[merged small][merged small][ocr errors][merged small][ocr errors]

In this Proportion, the firft Term, being the Radius, is fubtracted, by omitting ten in the Index of the Sum of the fecond and third Terms. And, for finding the Base, having the right Angle oppofite the Hypothenufe, and the Angle at C 53°. 6' oppofite the Bafe A B, the other Part required, ufe the following Proportion:

As the Radius, or Sine of the Angle at B,

Is to the Hypothenufe A C, 59.4,
So is the Sine of the Angle at C, 53°.6′,

To the Bafe AB, 47-5,

IO.

[ocr errors][merged small][merged small]

Which may be measured by the general Rule, Prob. 19. The Radius, being here the firft Term, is deducted, as in the laft Proportion.

Prob. 22. In the right-angled Triangle A B C, right-angled at B, given the Bafe A B 47.5, and the Angle at A 36°. 54, to find the Hypothenufe A C, and the Perpendicular BC.

Conftruction. Draw a Bafe-Line A B at Pleasure, and from the Scale, by the general Rule, Prob. 19, take 47.5, which fet from A to B; then, by Prob. 8, make an Angle of 36°.54 at A, thro' which draw the Hypo- A thenuse AC to a convenient Length;

C

B

laftly, raise a Perpendicular on the Point B, by Prob. 3, to interfect the Hypothenufe in the Point C, and the Triangle is completed.

[merged small][merged small][ocr errors][merged small][ocr errors]

The Angle at C is oppofite the given Bafe, and the right Angle, which is always known, is oppofite the Hypothenufe AC, one of the Parts required; whence,

Ae

As the Sine of the Angle at C, 53°.6',

Is to the Bafe A B, 47.5,

So is the Radius, or Sine of the Angle at B,

[blocks in formation]

To the Hypothenufe A C, 59-4,

Now, we have the fame Angle C opposite the given Base as before, and the given Angle A oppofite the Perpendicular B C, the other Part required; therefore,

As the Sine of the Angle at C, 53°. 6′,

9.902919

Is to the Bafe A B, 47.5,

1.676694

So is the Sine of the Angle at A, 36°.54,

9.778455

11.455149

9.902919

To the Ferpendicular B C, 35.66,

1.552230

The Hypothenufe and Perpendicular may be measured by the general Rule, Prob. 19.

Prob. 23. In the right-angled Triangle ABC, right-angled at B, given the Perpendicular BC 35.66, and the Angle at C 53°.6', to find the Hypothenufe AC, and Bafe A B.

Conftruction. Draw a Bafe-Line át Pleasure, and on the Point B erect a Perpendicular, by Prob. 3; from the diagonal Scale, by the general Rule, Prob. 19, fet off 35.66 from B to C; then, by Prob. 8, make an Angle at C of 53°.6', thro' which draw the

[ocr errors]

B

Hypothenufe A C, 'till it interfects the Bafe A B in the Point A, and the Triangle is completed.

[merged small][ocr errors][merged small][merged small][ocr errors][merged small]

The Angle at A is oppofite the given Perpendicular BC, and the Angle at B is oppofite to the Hypothenuse A C, one

of the Parts required; therefore,

As the Sine of the Angle at A, 36°. 54',

Is to the Perpendicular B C, 35.66,
So is the Radius, or Sine of the Angle at B,

10.

9.778455

1.552181

11.552181

9.778455

1.773726

To the Hypothenufe A C, 59.4,

The Hypothenuse may be measured by the general Rule, Prob. 19.

Now we have the right Angle at B oppofite the Hypothenufe found by the former Proportion, and the Angle at C 53°.6'; whence,

As the Radius,

Is to the Hypothenufe, 59.4,

10.

1.773786

So is the Sine of the Angle at C, 53°. 6',

9.902919

1.676705

To the Bafe A B, 47.5,

Which may be measured by the general Rule, Prob. 19. The firft Term being the Radius, I omit ten in the Sum of the fecond and third Numbers, as at Prob. 21.

Prob. 24. In the right-angled Triangle ABC, right-angled at B, given the Bafe A B 47.5, and the Angle at C 53°. 6', to find the Hypothenufe A C, and Perpendicular BC.

90°. 00'

53 6 Angle at C.

36

[ocr errors]
[ocr errors]

54 Angle at A. Conftruction. Draw the Bafe-Line A B at Pleasure; take 47.5 from the Scale, by the general Rule, Prob. 19, and fet from A to B; and on the Point B erect a Perpendicular, by Prob. 3, to any convenient Length; then make an Angle at A of 36°. 54,

C

B

the Complement of the given Angle C, by Prob. 8, and draw

the

the Hypothenufe AC 'till it interefects the Perpendicular in C, and the Triangle is completed.

Here is given the Angle C, and the Bafe A B oppofite to it; and the right Angle B, which is always known, is oppofite the Hypothenufe A C, one of the Parts required; whence,

As the Sine of the Angle at C, 53°.6′,

Is to the Bafe A B, 47.5,

So is the Radius, or Sine of the Angle at B,

[blocks in formation]

To the Hypothenuse A C, 59.4,

1.773775

Now we have the right Angle at B oppofite the Hypothenufe found by the laft Proportion, and the Angle at A 36°. 54 oppofite the Perpendicular B C, the Part required; whence,

As the Radius,

Is to the Hypothenuse A C, 59.4,
So is the Sine of the Angle at A, 36°. 54,

To the Perpendicular B C, 35.66,

10.

1.773786 9-778455

1.552241

Here the Radius being the firft Term, ten is omitted in the Index of the Sum of the other two Terms, as at Prob. 21. And the Hypothenufe and Perpendicular may be measured by the general Rule, Prob. 19.

Prob. 25. In the right-angled Triangle ABC, right-angled at B, given the Bafe AB 47.5, and the Perpendicular BC 35.66, to find the Angles A and C, and the Hypothenufe A C.

Conftruction. Draw a Bafe-Line A B

at Pleasure; take from the diagonal Scale 47.5, by the general Rule, Prob. 19, and fet from A to B ; at B erect a Perpendicular B C, on which, by the fame Rule, lay 35.66 from B to C; then draw the Hypothenufe A C, and the Triangle is completed.

B

« ΠροηγούμενηΣυνέχεια »