To make an angle equal to any number of degrees, suppose 42° 30.

RULE.

With the chord of 60 degrees in the compasses, on A describe an arch from the line AB, and from that line lay 42° 30' on the arch to D; then through the point D, draw AC, and it is done.

Note. To measure an angle, take the chord of 60° in the compasses, and with one foot in the angular point, make an arch from line to line; then take the arch in the compasses, apply it to the chord, which will shew the degrees; thus the preceding angle will measure 42o 30'.

PROBLEM IX.

To make an obtuse angle, equal to 102° 20'.

RULE.

With the chord of 60 degrees in the compasses, on B describe an arch, on which from C, set off 60 degrees to G, and from G, 42° 20′ to D; draw BD, and it is done.

D

102° 20

C

"PROBLEM X. .

The angles and hypothenuse given, to find the legs.

EXAMPLE.

The hypothenuse 121 perches, the angle opposite the base 54° 30'; consequently the other angle 35° 30' by position 2d. page 10; the base and perpendicular are required.

• RULE.

Draw the line CB, and on C, by Problem 8, make an angle equal to 35° 30', draw CA; take 121 perches in the compasses, from a scale of equal parts, and set it from C to A; then (by Problem 5) from A let fall the perpendicular AB; then the perpendicular AB, being taken in the compasses, and measured on the same scale, will be 70.25 perches, and the base CB, 98.5 perches, as required.

PROBLEM XI.

The angles, and one leg given, to find the hypothenuse, and the other leg.

EXAMPLE.

The angle opposite the perpendicular 33° 15'; the base 274 perches, to find the hypothenuse, and perpendicular.

RULE.

Draw CB, equal to 274 perches, from a scale of equal parts; upon B, erect a perpendicular, by Problem s; and on C, make an angle equal to 33° 15' by Problem 8; draw CA, and where it intersects the perpendicular, will be its length; then the hypothenuse CA, measured on the same scale, will be 327.6, and the perpendicular BC, 179.6 perches.

33 15

B

PROBLEM XII.

The hypothenuse, and one leg given, to find the angles, and the other leg.

EXAMPLE.

The perpendicular 69 chains, hypothenuse 150 chains; the base and angles are required.

RULE.

Draw the base, and on B ereet a perpendicular to A, equal to 69, from a scale of equal parts; from the same scale, take 150 in the compasses, and with one foot in A, let the other fall on the base, as at C; then the base, taken in the compasses, and applied to the same scale, will be 133, and the angle ACB, measured on the chord of 60 degrees, (by, the note to Problem 8) will be 27° 23′; consequently the other angle 62° 37′, by position 2, page 10.