9 Ademi Mth Dte: Pythgoren Theorem RIGHT ANGLE TRIANGLE - A right tringle is tringle with one 90 0 ngle. For exmple: In ny right-ngle tringle the side opposite to the right ngle is lled the Lbel the Hypotenuse in eh digrm bove. Pythgoren Theorem Formul: In ny right- ngled tringle, the squre of the hypotenuse is equl to the sum of the squres on the other two sides. b Solving for the Hypotenuse: b Exmple 1: Find the side length of the hypotenuse: b 4m 3m Exmple : Find the side length of the hypotenuse. 3mm 9mm Pge - 1 - of 6
9 Ademi Mth Dte: Prtie: Pythgoren Theorem Finding the Hypotenuse Find the length of eh hypotenuse (round to one deiml ple where neessry). b. 10mm 5mm 6m 3m. d. 4m 1m 6m 6m e.my neighbour hs squre vegetble grden whih is 3.5m by 3.5m. He wnts to put wlkwy digonlly through the grden to mke it esier to get the veggies in the middle. How long will his wlkwy be? f.an emergeny bot is on one side of wterwy nd there re ries of help on the other side. The wterwy is 0m wide nd the bot is bout 35 m down the wter wy from the people in need. Wht is the distne the bot must trvel if they go diretly (digonlly) to help? HELP! HELP! 0m BOAT 35m ANSWERS:. 6.7m, b. 17.9mm,. 1.6m, d. right tringle?, e.4.9m, f.40.3m Pge - - of 6
9 Ademi Mth Dte: Pythgoren Theorem Solving for side, other thn the hypotenuse To find side other thn the hypotenuse, you n use the sme formul or this rerrnged formul b b b Exmple 1: Find the vlue of the missing side: 5m 4m b Exmples: Find the length of eh missing side length: 8m 3.85m 15m 7.5m A box is 10 m long nd 5m wide. Wht is the length of the longest ski pole tht ould be pked to lie flt in the box? The window of burning building is 4 metres bove the ground. A ldder tht is 30m is ngled to reh the window nd the bse is out from the wll. How fr out from the wll is the ldder? Pge 3 of 6
9 Ademi Mth Dte: Prtie: Pythgoren Theorem - Drw digrm to help you identify the tringle nd the hypotenuse. 1. A 16 m long ldder lens ginst house. The foot of the ldder is 7m from the house. Find the height of the ldder from the ground, orret to the nerest tenth of meter.. Cn n umbrell, 1.3m long be pked flt into box 1.1m by 0.3m? Give resons for your nswer. 3. When on hike, Jen uts digonlly ross lrge retngulr field, 1.6km by 3.0 km, insted of keeping to the sidewlks. Wht distne does she sve by doing this? 4. A Pythgoren Triple onsists of three positive integers, b, nd, suh tht + b =. A well known exmple (3, 4, 5). This mens tht for ny of the tringles below, you n esily identify the vlue of the third side (notie the hypotenuse MUST be 5, the longest side). 3 5 3 5 4 4 ) Confirm tht this is Pythgoren Triple by solving for the missing side in on of the tringles bove. b) Ply round nd try to find nother Pythgoren Triple. There is formul for finding Pythgoren triples. Go online nd hek it out sometime. ANSWERS: 1. 14.4m,. No, mx 1.14m long umbrell, 3. 1.km, 4. vries Pge 4 of 6
9 Ademi Mth Dte: A Pythgoren Puzzle: Free the Hostge Prt A A friend of yours from mth lss is being held hostge by the UFPRLM (The United Front of People who re Resisting the Lerning of Mth). He is in the seond floor of house. You must go sve him, so tht mth lss n live on. You mnged to get into his room nd unite him. You her the ptors pproh the room so you must espe out of window. Fortuntely, you plnned for this possibility. You brought ldder, nd propped it up ginst the window before you went in. (see the digrm below). The window is 8m bove the ground, nd you pled the foot of the ldder 6m from the wll. How long is the ldder? wll 8m Ldder? m 6 m PART B After limbing down the ldder, you nd your friend must run ross field. Unfortuntely, you spot the ptors looking out of the window to find you. In order to void being spotted, you must hide behind tree. However, you don t wnt to lose time in your espe. Hene, you rwl long the shdow tht is used by the tree bloking the sun, until you reh lke.(see the digrm below) Use the informtion given to find how fr you must rwl (i.e. find the length of the shdow). Round to one deiml ple tree 14 m sun's ry's (from top of tree) 3 m Shdow? m Point of strt of Lke Pge 5 of 6
9 Ademi Mth Dte: A Pythgoren Puzzle: Free the Hostge Continued PART C You hve finlly mde it to the lst prt of your espe. You re t the edge of lke t point A. you must end up t point C. (See the digrm below). You hve hoie. You my drive from point A to point B, then from Point B to Point C or tke bot from Point A to Point C. One you mke it to Point C, you nd your friend re sved, nd n ontinue on to mth lss. The r trvels t 60 km per hour (beuse of ourse you obey the lw nd don t speed), nd the bot trvels t 35km per hour. A 10 km Lke B km C Answer the following questions: ) How fr (in kms) is the r ride? b) How fr (in kms) is the bot ride? ) You will need to tke the fstest route. Determine how long (in hours) eh trip will tke, then stte dis tn e whih method of trnsporttion is the best one to use. ( time ) speed ANSWERS: A) 10m, B)8.8m, C). 3km, b.4.1km,. 0.53hrs vs. 0.69hrs, fster to drive Pge 6 of 6