Real-Life Math
Police detectives have called you to a crime scene to help them
figure out what happened. A chambermaid found a dead person in a motel room.
It looks like the person was hit with a heavy object several times. The bright
yellow upholstered chairs are knocked over. Several magazines lie open in
a pool of thickening blood. And blood spots mark the walls and furniture.
You
look the scene over, noting where the body was found. It is quite a distance
from several of the blood spatters. You think the victim probably wasn't
killed where he was found, but how do you prove it?
You walk over to
the blood spray on the wall farthest from the victim. Then you look closely
at one of these blood spatters. Taking out your ruler, you measure it. The
width is 10 mm and the height is 39 mm. By dividing the width of the blood
splatter by its height then looking up the number in the trigonometry table,
you can figure out the angle that the blood hit the wall at. You're using
trigonometry to discover the sine of the angle.
You also take out a
wrinkled and well-used piece of paper from your wallet. It says:
PI
= 3.141592... (approximately 22/7 = 3.1428)
radians = degrees x PI / 180(deg to rad conversion)
degrees = radians
x 180 / PI(rad to deg conversion)
Â
Rad | Deg | Sin | Cos | Tan | Csc | Sec | Cot |
---|
.0000Â | 00Â | .0000Â | 1.0000Â | .0000Â | -----Â | 1.0000Â | -----Â | 90Â | 1.5707Â |
.0175Â | 01Â | .0175Â | .9998Â | .0175Â | 57.2987Â | 1.0002Â | 57.2900Â | 89Â | 1.5533Â |
.0349Â | 02Â | .0349Â | .9994Â | .0349Â | 28.6537Â | 1.0006Â | 28.6363Â | 88Â | 1.5359Â |
.0524Â | 03Â | .0523Â | .9986Â | .0524Â | 19.1073Â | 1.0014Â | 19.0811Â | 87Â | 1.5184Â |
.0698Â | 04Â | .0698Â | .9976Â | .0699Â | 14.3356Â | 1.0024Â | 14.3007Â | 86Â | 1.5010Â |
.0873Â | 05Â | .0872Â | .9962Â | .0875Â | 11.4737Â | 1.0038Â | 11.4301Â | 85Â | 1.4835Â |
.1047Â | 06Â | .1045Â | .9945Â | .1051Â | 9.5668Â | 1.0055Â | 9.5144Â | 84Â | 1.4661Â |
.1222Â | 07Â | .1219Â | .9925Â | .1228Â | 8.2055Â | 1.0075Â | 8.1443Â | 83Â | 1.4486Â |
.1396Â | 08Â | .1392Â | .9903Â | .1405Â | 7.1853Â | 1.0098Â | 7.1154Â | 82Â | 1.4312Â |
.1571Â | 09Â | .1564Â | .9877Â | .1584Â | 6.3925Â | 1.0125Â | 6.3138Â | 81Â | 1.4137Â |
.1745Â | 10Â | .1736Â | .9848Â | .1763Â | 5.7588Â | 1.0154Â | 5.6713Â | 80Â | 1.3953Â |
.1920Â | 11Â | .1908Â | .9816Â | .1944Â | 5.2408Â | 1.0187Â | 5.1446Â | 79Â | 1.3788Â |
.2094Â | 12Â | .2079Â | .9781Â | .2126Â | 4.8097Â | 1.0223Â | 4.7046Â | 78Â | 1.3614Â |
.2269Â | 13Â | .2250Â | .9744Â | .2309Â | 4.4454Â | 1.0263Â | 4.3315Â | 77Â | 1.3439Â |
.2443Â | 14Â | .2419Â | .9703Â | .2493Â | 4.1336Â | 1.0306Â | 4.0108Â | 76Â | 1.3265Â |
.2618Â | 15Â | .2588Â | .9659Â | .2679Â | 3.8637Â | 1.0353Â | 3.7321Â | 75Â | 1.3090Â |
.2793Â | 16Â | .2756Â | .9613Â | .2867Â | 3.6280Â | 1.0403Â | 3.4874Â | 74Â | 1.2915Â |
.2967Â | 17Â | .2924Â | .9563Â | .3057Â | 3.4203Â | 1.0457Â | 3.2709Â | 73Â | 1.2741Â |
.3142Â | 18Â | .3090Â | .9511Â | .3249Â | 3.2361Â | 1.0515Â | 3.0777Â | 72Â | 1.2566Â |
.3316Â | 19Â | .3256Â | .9455Â | .3443Â | 3.0716Â | 1.0576Â | 2.9042Â | 71Â | 1.2392Â |
.3491Â | 20Â | .3420Â | .9397Â | .3640Â | 2.9238Â | 1.0642Â | 2.7475Â | 70Â | 1.2217Â |
.3665Â | 21Â | .3584Â | .9336Â | .3839Â | 2.7904Â | 1.0711Â | 2.6051Â | 69Â | 1.2043Â |
.3840Â | 22Â | .3746Â | .9272Â | .4040Â | 2.6695Â | 1.0785Â | 2.4751Â | 68Â | 1.1868Â |
.4014Â | 23Â | .3907Â | .9205Â | .4245Â | 2.5593Â | 1.0864Â | 2.3559Â | 67Â | 1.1694Â |
.4189Â | 24Â | .4067Â | .9135Â | .4452Â | 2.4586Â | 1.0946Â | 2.2460Â | 66Â | 1.1519Â |
.4363Â | 25Â | .4226Â | .9063Â | .4663Â | 2.3662Â | 1.1034Â | 2.1445Â | 65Â | 1.1345Â |
.4538Â | 26Â | .4384Â | .8988Â | .4877Â | 2.2812Â | 1.1126Â | 2.0503Â | 64Â | 1.1170Â |
.4712Â | 27Â | .4540Â | .8910Â | .5095Â | 2.2027Â | 1.1223Â | 1.9626Â | 63Â | 1.0996Â |
.4887Â | 28Â | .4695Â | .8829Â | .5317Â | 2.1301Â | 1.1326Â | 1.8807Â | 62Â | 1.0821Â |
.5061Â | 29Â | .4848Â | .8746Â | .5543Â | 2.0627Â | 1.1434Â | 1.8040Â | 61Â | 1.0647Â |
.5236Â | 30Â | .5000Â | .8660Â | .5774Â | 2.0000Â | 1.1547Â | 1.7321Â | 60Â | 1.0472Â |
.5411Â | 31Â | .5150Â | .8572Â | .6009Â | 1.9416Â | 1.1666Â | 1.6643Â | 59Â | 1.0297Â |
.5585Â | 32Â | .5299Â | .8480Â | .6249Â | 1.8871Â | 1.1792Â | 1.6003Â | 58Â | 1.0123Â |
.5760Â | 33Â | .5446Â | .8387Â | .6494Â | 1.8361Â | 1.1924Â | 1.5399Â | 57Â | .9948Â |
.5934Â | 34Â | .5592Â | .8290Â | .6745Â | 1.7883Â | 1.2062Â | 1.4826Â | 56Â | .9774Â |
.6109Â | 35Â | .5736Â | .8192Â | .7002Â | 1.7434Â | 1.2208Â | 1.4281Â | 55Â | .9599Â |
.6283Â | 36Â | .5878Â | .8090Â | .7265Â | 1.7013Â | 1.2361Â | 1.3764Â | 54Â | .9425Â |
.6458Â | 37Â | .6018Â | .7986Â | .7536Â | 1.6616Â | 1.2521Â | 1.3270Â | 53Â | .9250Â |
.6632Â | 38Â | .6157Â | .7880Â | .7813Â | 1.6243Â | 1.2690Â | 1.2799Â | 52Â | .9076Â |
.6807Â | 39Â | .6293Â | .7771Â | .8098Â | 1.5890Â | 1.2868Â | 1.2349Â | 51Â | .8901Â |
.6981Â | 40Â | .6428Â | .7660Â | .8391Â | 1.5557Â | 1.3054Â | 1.1918Â | 50Â | .8727Â |
.7156Â | 41Â | .6561Â | .7547Â | .8693Â | 1.5243Â | 1.3250Â | 1.1504Â | 49Â | .8552Â |
.7330Â | 42Â | .6691Â | .7431Â | .9004Â | 1.4945Â | 1.3456Â | 1.1106Â | 48Â | .8378Â |
.7505Â | 43Â | .6820Â | .7314Â | .9325Â | 1.4663Â | 1.3673Â | 1.0724Â | 47Â | .8203Â |
.7679Â | 44Â | .6947Â | .7193Â | .9657Â | 1.4396Â | 1.3902Â | 1.0355Â | 46Â | .8029Â |
.7854Â | 45Â | .7071Â | .7071Â | 1.0000Â | 1.4142Â | 1.4142Â | 1.0000Â | 45Â | .7854Â |
Â
Using these three pieces of information, at what
angle did the blood hit the wall?