(5) 24.995-25 ft. nearly, 17 559 ft., 65° 59′ 42′′.

(1) A=51°18′21′′, C=88°41′39′′; or A = 128° 41′39′′, C=11° 18′21′′. (2) B=70° 0′ 56′′, C=59° 59′ 4′′; or, B=109° 59′ 4′′, C=20° 0′ 56′′. (3) B=38° 38′ 24′′, C=91° 21′ 36′′, c=155.3. (4) 61° 16' 10", (5) A=72° 4′48′′, B=41° 56′ 12′′; or, A=107° 55′ 12′′,

B=6°5′ 48′′, b=17.56.

(6) ẞ is ambiguous; 60-3893 ft.

LXX. Page 220.

The angles are given correct to the nearest second.

(10) A=66°27′ 48′′, B=12°55′12′′. (11) A=92°12′53′′,B=35° 37′ 7′′. (12) B=29°1′40′′, C=74°55′50′′. (13) B=70°35′24′′; or, 109° 24′36′′. (14) B=51°56′17′′; or, 128°3′43′′. (16) Very nearly 90°.

(17)

(15) B=62°6′10′′; or, 117° 53′ 50′′. 1319-6 yds.

LXXII. Page 229.

(15) To find the point E in an unlimited straight line CE at which a finite straight line AB subtends the greatest angle, a circle must be described passing through A and B, and touching the line CE in the point E. In (15) the centre of the circle lies vertically above E, and in the horizontal line through the middle point of AB.

LXXVI. Pages 253-256.

(10) -(x+y+z) (y + z− x) (z+x − y) (x + y − z).

{6nπ − 2π+ ( − 1)TMπ}.

+cot-1 {tan +8 m sin 8+n sin a

2

n sin a -m sin ß)'

(vi) sin 40. cos

sin

=

=0.

2

(vii) sin 80. ₤in 40=0.

2

(21) 223-17.

in the case of an equilateral triangle.

(2) The sides of a triangle are as 2:√6:1+/3, find the angles.

(3) The sides of a triangle are as 4, 2√2, 2(√3 − 1), find the angles.

(4) Given C=120o, c=√19, a=2, find b.

(5) Given A=60o, b=4√7, c=6° √7, find a.

(6) Given A=45o, B=60° and a=2, find c.

(7)

angle.

The sides of a triangle are as 7: 8: 13, find the greatest

(8) The sides of a triangle are 1, 2, √7, find the greatest angle.

(9) The sides of a triangle are as ab: (a2 + ab − b2), find the greatest angle.

(10) When a : b c as 3:4: 5, find the greatest and least angles; given cos 36° 52′ ='8.

(11) If a=5 miles, b=6 miles, c=10 miles, find the greatest angle. [cos 49° 33′ = •65.]

(12) If a=4, b=5, c=8, find C; given that cos 54°54′='575. (13) The sides of a triangle are 7, 8, 13, find the greatest angle.

(14) Given C=18°, a=√5 +1, c=√5 - 1, find the other angles.

(15) If b=3, C=120o, c=√13, find a and the sines of the other angles.

(16) Given A-105°, B=45°, c=/2, solve the triangle.

(17) Given B=75o, C=30°, c=√8, solve the triangle.
(18) Given B=45o, c=√75, b=√50, solve the triangle.

(19) Given B=30°, c=150, b=50/3, show that of the two triangles which satisfy the data one will be isosceles and the other right-angled. Find the third side in the greatest of these triangles.

(20) Is the solution ambiguous when B=30°, c=150, b=75?

(21) If the angles adjacent to the base of a triangle are 221o and 11210, show that the perpendicular altitude will be half the base.

(22) If a=2, b=4-2√3, c=√6 (3-1), solve the triangle. (23) If A-90, B=45°, b=√6, find c.

(24) Given B=15°, b=√3-1, c=√3+1, solve the triangle.

(25) Given sin B=·25, a=5, b=2·5, find A. Draw a figure to explain the result.

(26) Given C=15o, c=4, a=4+√48, solve the triangle.

(27) Two sides of a triangle are 3/6 yards and 3 (√3+1) yards, and the included angle 45o, solve the triangle.

(28) If C=30°, b=100, c=45, is the triangle ambiguous?
(29) Prove that if A=45o and B=60° then 2c=a(1+√3).

(30) The cosines of two of the angles of a triangle are and, find the ratio of the sides.

(8) 120o. (9) 120o.

(13) 120o. (14)
(16) C=30°, a=√3+1, b=2.
(18) C=60° or 120o.

(10) 90o, 36° 52'. (11) 130° 27'. A=54° or 126o, B=108° or 36o. (15) a=1. (17) A=75°, a=b=√3+1.

(12) 125° 6'.

(22) A=105°, C=60, B=15.

(23)

√3(√5+1).

(24) A=90° or 60o, C=75° or 105o, a=2√2 or √/6. or 150o.

(26) A=45° or 135°, B=30° or 120°, b=√2 (1+√3)

(25) 30o

or √6 (1+√3). (27) 60°, 75o, 6 yds.

(30) 15:83:4√5+6.

(28) It is impossible.

CAMBRIDGE: PRINTED BY C. J. CLAY, M.A. & SON, AT THE UNIVERSITY PRESS.