Plane trigonometry, by S.L. Loney.

AREA OF A TRIANGLE.

227

EXAMPLES. XXXV.
Find the area of the triangle ABC when
1. a=13, b=14, and c=15. 2. a=18, b=24, and c=30.
3. a=25, b=52, and c=63. 4. a=125, b=123, and c=62.
5. a=15, b=36, and c=39. 6. a=287, b=816, and c=865.
7. a=35, b=84, and c =91.
8. a=,3, b=/2, and c-^ 2'
9. If B=45~, C=600, and a=2 (/3+ 1) inches, prove that the area
of the triangle is 6 + 2,/3 sq. inches.
10. The sides of a triangle are 119, 111, and 92 yards; prove that its
area is 10 sq. yards less than an acre.
11. The sides of a triangular field re 242, 1212 and 1450 yards;
prove that the area of the field is 6 acres.
12. A workman is told to make a triangular enclosure of sides 51, 41,
and 21 yards respectively; having made the first side one yard too long,
what length must he make the other two sides in order to enclose the
prescribed area with the prescribed length of fencing?
13. Find, correct to '0001 of an inch, the length of one of the equal
sides of an isosceles triangle on a base of 14 inches having the same area
as a triangle whose sides are 13-6, 15, and 15'4 inches.
sin B sin C
14. Prove that the area of a triangle is a2 sin C
If one angle of a triangle be 60~, the area 10V/3 square feet, and the
perimeter 20 feet, find the lengths of the sides.
3
15. The sides of a triangle are in A.P. and its area is - ths of an
equal triangle of the same perimeter; prove that its sides are in the ratio
3: 5: 7, and find the greatest angle of the triangle.
16. In a triangle the least angle is 45~ and the tangents of'the angles
are in A.P. If its area be 3 square yards, prove that the lengths of the
sides are 3V5, 6~/2, and 9 feet, and that the tangents of the other angles
are respectively 2 and 3.
15-2