Ex. 229. What sort of figures are the ends of the prism in fig. 67 What are the sides? Ex. 230. Draw its net. Ex. 231. What is the number of edges, faces, and corners ? Ex. 232. What is the greatest number of edges, faces, and corners you can see at one time? Ex. 233. Make sketches of a regular hexagonal prism from three different points of view. DRAWING TO SCALE. When drawing a map, or plan, to scale you should always begin by making a rough sketch showing the given dimensions, and then work from the sketch. The bearing of a place A from a second place B is the point of the compass towards which a man at B would be facing if he were looking in the direction of A. By "N. 10° W." or "10° W. of N." is meant the direction in which you would be looking if you first faced due north and then turned through an angle of 10° towards the west. Ex. 234. A is 2.5 miles W. of B, and C is 4.5 miles S. of A. What is the distance from B to C? What is the bearing of B from C, and of C from B? (Scale 1 mile to 1 inch.) Ex. 235. G is 7.5 miles S. of H, and 10 miles W. of K. What is the distance and bearing of K from H? (Scale 1 mile to 1 cm.) Ex. 236. X is 17.5 miles N.W. of Y, Y is 23 miles N.E. of Z. What is the distance and bearing of X from Z? (Scale 10 miles to 1 inch.) Ex. 237. P is 64 miles W. of Q, R is due N. of Q; if PR is 72 miles, what is QR? What is the bearing of P from R? (Scale 10 miles to 1 cm.) Ex. 238. Draw a plan of a room 30 ft. by 22 ft.; find the distances between opposite corners. (Scale 2 ft. to 1 cm.) Ex. 239. Exeter is 48 miles W. of Dorchester, and Barnstaple is 35 miles N.W. of Exeter. What is the distance and bearing of Barnstaple from Dorchester? (Scale 10 miles to 1 in.) Ex. 240. Rugby is 44 miles N. of Oxford, and Reading is 24 miles S. 30° E. of Oxford. Find the distance from Rugby to Reading. (Scale 10 miles to 1 in.) Ex. 241. Southampton is 72 miles W. 37° S. of London, Gloucester is 15° N. of W. from London, and 29° W. of N. from Southampton. Find the distance between Southampton and Gloucester. (Scale 10 miles to 1 cm.) In the following exercises, use any suitable scale; always state what scale you use. Ex. 242. Draw a plan of a rectangular field 380 yards by 270 yards. What is the distance between the opposite corners? Ex. 243. The legs of a pair of compasses are 10 cm. long. I open them to an angle of 35°. What is the distance between the compass points? Ex. 244. Two blockhouses are known to be 1000 yards apart, and one of them is due E. of the other. A party of the enemy are observed by one blockhouse in a N.W. direction, and at the same time by the other in a N.E. direction. How far are the enemy from each blockhouse? Ex. 245. A and B are two buoys 800 yards apart, B due N. of A. A vessel passes close to B, and steering due E., observes that after 5 minutes the bearing of A is 33° S. of W. Find the distance the vessel has moved. Ex. 246. Stafford is 27 miles from Derby and the same distance from Shrewsbury, and the three towns are in a straight line. Birmingham is 40 miles from Shrewsbury and 35 from Derby. How far is Stafford from Birmingham? Ex. 247. A buoy is moored by a cable 55 feet long; at low tide the distance between the extreme positions the buoy can occupy is 100 feet. What will be the distance between the extreme positions when the water is 24 feet higher? Ex. 248. Two ships sail from a port, one due N. at 15 miles an hour, the other E.N.E.; at the end of half an hour they are in line with a lighthouse which is 11 miles due E. of the port. At what rate does the second ship sail? Ex. 249. A donkey is tethered to a point 20 feet from a long straight hedge; he can reach a distance of 35 feet from the point to which he is tethered. How much of the hedge can he nibble? Ex. 250. A is a lighthouse. apart. B and C are two ships 3.5 miles B is due north of A, C due east of B, and C northFind the distance of both ships from the light east of A. house. Ex. 251. A man standing on the bank of a river sees a tree on the far bank in a direction 20° W. of N. He walks 200 yards along the bank and finds that its direction is now N.E. If the river flows east and west, find its breadth. Ex. 252. A ferry-boat is moored by a rope 30 yards long to a point in the middle of a river. The rope is kept taut by the current. What angle does it turn through as the boat crosses the river, whose width is 30 yards? Ex. 253. The case of a grandfather clock is 16 inches wide; the pendulum is hung in the middle of the case and its length is 39 inches. Assuming that the end of the pendulum swings to within 3 inches of each side of the case, find the angle through which it swings. Ex. 254. Brixham is 4.6 miles N.E. of Dartmouth, Torquay is 4 miles N. of Brixham, Totnes is 7.4 miles W. 15° S. of Torquay; what is the distance and bearing of Totnes from Dartmouth? Ex. 238. Draw a plan of a room 30 ft. by 22 ft.; find the distances between opposite corners. (Scale 2 ft. to 1 cm.) Ex. 239. Exeter is 48 miles W. of Dorchester, and Barnstaple is 35 miles N.W. of Exeter. What is the distance and bearing of Barnstaple from Dorchester? (Scale 10 miles to 1 in.) Ex. 240. Rugby is 44 miles N. of Oxford, and Reading is 24 miles S. 30° E. of Oxford. Find the distance from Rugby to Reading. (Scale 10 miles to 1 in.) Ex. 241. Southampton is 72 miles W. 37° S. of London, Gloucester is 15° N. of W. from London, and 29° W. of N. from Southampton. Find the distance between Southampton and Gloucester. (Scale 10 miles to 1 cm.) In the following exercises, use any suitable scale; always state what scale you use. Ex. 242. Draw a plan of a rectangular field 380 yards by 270 yards. What is the distance between the opposite corners? Ex. 243. The legs of a pair of compasses are 10 cm. long. I open them to an angle of 35°. What is the distance between the compass points? Ex. 244. Two blockhouses are known to be 1000 yards apart, and one of them is due E. of the other. A party of the enemy are observed by one blockhouse in a N.W. direction, and at the same time by the other in a N.E. direction. How far are the enemy from each blockhouse? Ex. 245. A and B are two buoys 800 yards apart, B due N. of A. A vessel passes close to B, and steering due E., observes that after 5 minutes the bearing of A is 33° S. of W. distance the vessel has moved. Find the Ex. 246. Stafford is 27 miles from Derby and the same distance from Shrewsbury, and the three towns are in a straight Birmingham is 40 miles from Shrewsbury and 35 from Derby. How far is Stafford from Birmingham? line. erves 1 the same aight from Ex. 247. A buoy is moored by a cable 55 feet long; at low tide the distance between the extreme positions the buoy can occupy is 100 feet. What will be the distance between the extreme positions when the water is 24 feet higher? Ex. 248. Two ships sail from a port, one due N. at 15 miles an hour, the other E.N.E.; at the end of half an hour they are in line with a lighthouse which is 11 miles due E. of the port. At what rate does the second ship sail? Ex. 249. A donkey is tethered to a point 20 feet from a long straight hedge; he can reach a distance of 35 feet from the point to which he is tethered. How much of the hedge can he nibble? Ex. 250. A is a lighthouse. B and C are two ships 3.5 miles apart. B is due north of A, C due east of B, and C northeast of A. Find the distance of both ships from the lighthouse. Ex. 251. A man standing on the bank of a river sees a tree on the far bank in a direction 20° W. of N. He walks 200 yards along the bank and finds that its direction is now N.E. If the river flows east and west, find its breadth. Ex. 252. A ferry-boat is moored by a rope 30 yards long to a point in the middle of a river. The rope is kept taut by the current. What angle does it turn through as the boat crosses the river, whose width is 30 yards? Ex. 253. The case of a grandfather clock is 16 inches wide; the pendulum is hung in the middle of the case and its length is 39 inches. Assuming that the end of the pendulum swings to within 3 inches of each side of the case, find the angle through which it swings. Ex. 254. Brixham is 4.6 miles N.E. of Dartmouth, Torquay is 4 miles N. of Brixham, Totnes is 7.4 miles W. 15° S. of Torquay; what is the distance and bearing of Totnes from Dartmouth? |