MATH EXTRA CREDIT PROJECT BY: DALIA YUDEWITZ – PERIOD 3 AND AVITA SHARMA – PERIOD 4 MS. STUPP

INDIRECT MEASUREMENT Indirect Measurement is the process of measuring an object that is not easily measured indirectly. Dalia is setting up.

MATERIALS MIRROR COMPUTER RULER PENCIL & PAPER OBJECT IMPOSSIBLE TO MEASURE WITH A RULER Yardstick Mirror Pencil, calculator, paper, brains poll camera computer

SETUP First put the mirror on the floor. Then walk backward until you can see the top of the object. Measure your distance from the mirror, and the distance from the object to the mirror. Measure your height from your eyes downward. On a sheet of paper, draw the two triangles formed and plug in the measurements collected, where x will be the object’s height. Solve for x by cross multiplying.

WORK AS YOU CAN SEE, IT IS ALMOST IMPOSSIBLE TO MEASURE THIS POLE WITH A RULER.

Our work POLEPOLE 100”17” Pole- x ft. tall Distance from pole to mirror- 100in. Dalia (eyes down)- 65 in tall Distance from Dalia to mirror- 17in Not in any way drawn to scale. X F t. T A L 65”65” 1.Convert all units to inches. My height (from eyes down) 5’5”= 65”{ Dist. Between Dalia+mirror 1’5”=17”{ Dist. Between pole+mirror 8’4”=100” 2.Draw diagram (shown above) 3. Set up proportion to figure out height of pole. x/100=65/17 (further explanation in next slide) 4.Solve 17x= Convert answer to inches, /12= Round answer to get about 31.9 ft.

REVIEW 8ft & 4in (100in) Distance between pole and mirror 1ft & 5in (17in) Distance between mirror and Dalia 5ft & 5in (65in) Height of Dalia from eyes down DISTANCE OF POLE = APPROXAMATELY 31.9 FT We are now going to review everything we did. YAY!!!!!!!!!!! We converted our units to inches so every measurement would be in compatible units. Our setup formed two similar triangles. The larger being the triangle formed by the pole and pole’s distance to the mirror, the smaller formed by Dalia and her distance from the mirror. To arrange the proportions, we put leg A (pole) of the larger triangle over leg B of the same triangle and set it equal to leg A of the smaller triangle over leg B of the smaller triangle. We then used the Cross- Products property to solve the proportion. Our last step was converting the units back to feet because feet would be the more practical unit to use to express the pole’s height.

Results The answer is logical, so we can assume the height of the poll is about 31.9 ft. Even so, we have to make sure… Avita graciously volunteered to measure the light poll. She got a nice view and proved that we CAN use similar triangles to figure out the unknown length of an object.

BLOOPERS Some of our trial pictures didn’t turn out as good as we hoped. Nevertheless, we thought it not necessary to leave them out all together.

CREDITS Starring: Avita Sharma and Dalia Yudewitz Directed by: Dalia and Avita Camera People: Avita and Dalia Measurer: Avita Calculations: Dalia and Avita Slide Show: Avita and Dalia Editor: Dalia No animals were harmed in the making of this presentation ©SharmaYudewitzExtraCreditProject 2009 Made on location at the Weston Library Park

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