Plane and solid geometry . sur-face has an area of 216 square feet are 95°, 105°, and 130°. Find thenumber of square feet in the area of the triangle. , Ex. 1573. In a sphere whose diameter is 16 inches, find the area ofa triangle whose angles are 70°, 86°, and 120°. Ex. 1574. The angles of a spherical triangle are 60°, 120°, and 160°,and its area is 1004 square inches. Find the radius of the sphere. (Use Ex. 1575. The area of a spherical triangle is 90 spherical degrees,and the angles are in the ratio of 2, 3, and 5. Find the angles. Ex. 1576. Find the angle (1) of an equilateral spherical tr
Plane and solid geometry . sur-face has an area of 216 square feet are 95°, 105°, and 130°. Find thenumber of square feet in the area of the triangle. , Ex. 1573. In a sphere whose diameter is 16 inches, find the area ofa triangle whose angles are 70°, 86°, and 120°. Ex. 1574. The angles of a spherical triangle are 60°, 120°, and 160°,and its area is 1004 square inches. Find the radius of the sphere. (Use Ex. 1575. The area of a spherical triangle is 90 spherical degrees,and the angles are in the ratio of 2, 3, and 5. Find the angles. Ex. 1576. Find the angle (1) of an equilateral spherical triangle,(2) of a lune, each equivalent to one third the surface of a sphere. Ex. 1577. Find the angle of a lune equivalent to an equilateralspherical triangle one of whose angles is 84°. 456 SOLID GEOMETRY Proposition XXVI. Theorem 993. The area of a spherieal polygon, expressed inspJierieal degrees, is equal to tlve suin of its angles dimin-isJied by 180^ taken as many times less two as the poly-gon has sides. c. Given spherical polygon ^^CZ) ... with n sides; denote thesum of its angles by T. To prove area of polygon ABCD ..., expressed in sphericaldegrees, = T—{n — 2)180. Argument 1. From any vertex such as A, draw all possible diagonals of the polygon,forming n — 2 spherical A, I, II, etc. 2. Then, expressed in spherical degrees, AI=(Z 1 + Z 2 4-^3)-180; A 11= (Z 4 + Z 5 -h Z 6) - 180; etc.•. A I + A II + ••• = 2^- {n - 2)180.•. area of polygon ABCD ... = r-(?i-2) 180. 1. Reasons§ 937. 2. § 990. 3. § 54, 2. 4. § 309. Ex. 1578. Prove Prop. XXVI by using a figure similar to that usedin § 21G. Ex. 1579. Find the area of a spherical polygon whose angles are 80^,92°, 120°, and 140^, in a sphere whose radius is 8 inches. Ex. 1580. Pind the angle of an equilateral spherical triangle equiva-lent to a si)lurical pentagon whose angles are 90°, 100°, 110°, 130°, and 140°. Ex. 1581. Find one ansjle of an equiansjular spherical hexasjone(
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