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Vánoční matematika pro 8. ročník - anglicky

Christmas Maths – Pythagoras theorem – form 8.B from school Kosmonautů 15, Ostrava

1) Children at Christmas ride down a hill on a sledge. Count the height of the hill if they ride 70 metres and the distance at the bottom is 50 metres.
2) Santa Claus wants to give presents to children. He has flown the distance 400 km and reached the cruising altitude 50 km. How many kilometres was it on the ground?
3) There are three Christmas bulbs on the Christmas tree. The distance between the red and yellow ones is 13 cm; the distance between the yellow and blue ones is 16 cm. What is the distance between the blue and red Christmas bulbs?
4) Santa Claus wanted to give presents to children. He flew 600 km to reach altitude 100 km. How many kilometres did he have to fly to reach altitude 60 km? Is it possible to solve it with the Pythagoras theorem? Help: use the ratio.
Ježíšek chtěl rozdat dárky dětem. Uletěl vzdálenost 600 km ve výšce 100 km. Kolik km musel uletět, než se dostal 60 km? Lze to řešit pomocí Pythagorovy věty? Napovíme: využij poměr.
5a) Father wants to hang up mistletoe on the light so he takes the stepladder. The base is 4.4 m and the side is 7.7 m long. What is the length of the stepladder?
5b) Mother is baking Christmas rolls. She has 25 rolls, Johnny comes to help her and eats 9.5 rolls. How many rolls are left on the baking tray?
6) St. Nicolas and Angel are standing at the end of one leg of the right-angled triangle. Where must Devil stand if he wants to stand at the last corner of the right-angled triangle? Help him find his place if a = 7,5 cm and b = 9,2 cm, use the Pythagoras theorem.
7) Ann wants to calculate the height of the Santa hat. The side measures 17 cm and the base is 14 cm.
8) Father is calculating the height of the Christmas tree. Will you help him? The base is 20 cm long and the side is 120 cm long.
9a) Father has climbed up the ladder to hang up Christmas lights. The ladder is 2.5 m long. The base is 1.3 m. What is the height of the ladder?
9b) St. Nicolas, a devil and an angel went to see children. They had to visit two houses. One was 2.5 km down the hill and the other house was 1.5 km to the left from the first house. The weather was bad so they decided to take a shortcut to get back after visiting the second house. a) How long is the shortcut? b) How many metres is the shortcut shorter than the road?
10) Boys are sledging on a hill which slope is 10 metres long and the base measures 11 metres. What is the height of the hill? It is not possible calculate with the Pythagoras theorem, why?
11) Carollers must visit two houses; their house is at the right angle corner and all the houses are situated at the corners of a right angled triangle. The distance to the first house is 300 metres. Then they will use a short cut through the park to the second house which is 500 metres. How many metres are left to get back home?