2. The radius of the circle circumscribed about a triangle

Let O be the centre of the circumscribed circle, and OD be drawn perpendicular to the side BC.

1. If the sides of a triangle are 56, 65, and 33 ft., find the greatest angle and the area of the triangle.

2. The sides of a parallelogram are 15 and 17 ft., and one of its smaller angles is 42°. Find its area and the lengths of its diagonals.

3. The sides of a triangular field are 119, 111, and 92 yds. Show that its area is 10 sq. yds. less than an acre.

4. Two angles of a triangle are 42° and 68°, respectively, and the least side is 20 ft. Find its area.

5. The sides of a triangle are 11 ft., 13 ft., and 18 ft., respectively. Find the radius of the inscribed circle.

6. Two sides of a triangle are 21 ft. and 24 ft., respectively, and the included angle is 110°. Find its area.

MENSURATION FORMULAS

In the following table, unless otherwise specified, A denotes the area; a, b, c, the sides of a triangle; b, the base; c, the hypotenuse of a right triangle; r, the radius; d, the diameter; 7, the lateral edge; s, the slant height; C, the circumference; P, the perimeter; L, the lateral area; V, the volume.

INDEX TO DEFINITIONS

Altitude, 197, 198, 311, 329.