TRIANGLE 



5877 



TRIASSIC SYSTEM 



H2 = 10000 



H = V 10000 

 H = 100 



Note : The diagonal of the field is the hypote- 

 nuse of a right triangle. 



2. A baseball diamond is 90 feet square. 

 How far is it from first to third base? Ans. 

 127.27+ feet. 



3. How far out from a wall must a 12%-foot 

 ladder be placed to reach a window 10 feet 

 from the ground? 



Solution : 



H2-A2 + B2 

 (121/2 ) 2 = 10 2 + -B2 

 156.25 = 100 + J32 



B2 = 156.25 100 

 B2 = 56.25 

 B = ^56.25 

 B = 7.5 

 Distance = 7. 5 ft. 



When the base and altitude of a right tri- 

 angle-are 3 and 4 or 4 and 3, the hypotenuse 

 is 5, since 3 2 +4 2 =5 2 . Therefore, when the base 

 and altitude are in the ratio 3, 4 or 4, 3, the 

 three sides are in the ratio 3, 4, 5. This fact 

 has been used as the basis for laying out 

 "square corners." The so-called "rope stretch- 

 ers" of Egypt are said to have used it in laying 

 out the foundations of the pyramids, and the 

 builder to-day uses it to lay out a foundation. 

 A line 8 feet long is stretched from the desired 

 corner point along in the direction one wall is 

 to take; a line 6 feet long is fastened at the 

 same point and stretched to make a right angle 

 with the first line; a 10-foot pole is laid from 

 the outer extremity of the 8-foot line extend- 

 ing toward the outer extremity of the 6-foot 

 line, which is moved until the 10-foot pole 

 just fits between the extremities of the lines. 

 Then the corner is a right angle. 



When the base and altitude are in the ratio 

 3, 4 or 4, 3, it is very easy to know the hypote- 

 nuse; for example: 



48 



Find n in each of the following: 



15 

 18 



n 



n 

 27 

 44 

 51 



1% 



A 

 20 

 24 

 40 

 27 



n 



n 

 68 



2 



n 



n 



50 



45 



45 



53 



n 



up a large part of the study of trigonometry. 

 One of the objects of trigonometry is to find 

 heights and distances without actually measur- 

 ing them, as heights of mountains, widths of 

 bodies of water, distance of vessels out at sea, 

 astronomical distances, etc. 



Area of Triangles, (a) When base and alti- 

 tude are known, to find area, multiply base by 

 one-half altitude. (For full discussion of this, 

 see MENSURATION.) 



(b) When sides are known but altitude is 

 unknown, to find area, find one-half the sum of 

 the sides ; ' from this subtract each side sepa- 

 rately. Find the product of half the sum of 

 the sides and the three remainders found above. 

 Take the square root of this product. 



Letting s stand for half the sum of the sides, 

 and a, b and c for the sides respectively, the 

 law is stated thus: 



Area &= \/s(s a) (s b) (s c) 



Problem. Find the area of a triangular field 

 whose sides are 21 rods, 28 rods and 35 rods. 



Solution : 



21 + 28 + 3; 

 2 



= 42 



Triangular Measurements. The relations 

 among the sides and angles of triangles make 



Area &= ys(s-a) (s b) (s c) 

 Area in sq. rd. = \f 42 (42 21) (42 28) (42 35) 

 Area in sq. r d. = V42X21X14X? = 294 



The student will find many opportunities out- 

 of-doors for making and testing square corners 

 by the rope-stretcher method, and for finding 

 the relations between the sides of the right tri- 

 angle. A.H. 



TRIASSIC SYSTEM, trias'ik sis' tern, in 

 geology, the rock formations of the oldest di- 

 vision of geologic time in the Mesozoic Era, 

 extending from the Permian Period to the 

 Jurassic (see diagram, page 2439). In the east- 

 ern part of the United States the Triassic for- 

 mation is found from Connecticut to North 

 Carolina. The rock consists chiefly of con- 

 glomerate (which see) and sandstone. The 

 sandstone of the Connecticut Valley and New 

 Jersey, so highly prized for building, was formed 

 at this time and is sometimes known as the 

 New Red Sandstone. The Palisades of the 

 Hudson also belong to this period. During 

 this and the Jurassic Period the reptiles at- 

 tained their greatest size and development, and 

 the older geologists frequently called the Tri- 

 assic the Age of the Reptiles. Lizardlike ani- 

 mals of gigantic size were common on land, 

 and the sea teemed with other monsters which 

 fed upon fish and upon each other. Fossils are 

 found in considerable numbers. 



