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Similarity using indirect measurements updated 3 19-14
 

Similarity using indirect measurements updated 3 19-14

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    Similarity using indirect measurements updated 3 19-14 Similarity using indirect measurements updated 3 19-14 Presentation Transcript

    • Warm Up Convert each measurement. 1. 6 ft 3 in. to inches 2. 5 m 38 cm to centimeters Find the perimeter and area of each polygon. 3. square with side length 13 cm 4. rectangle with length 5.8 m and width 2.5 m 75 in. 538 cm P = 52 cm, A =169 cm2 P =16.6 m, A = 14.5 m2 GT Geometry
    • Indirect measurement is any method that uses formulas, similar figures, and/or proportions to measure an object. The following example shows one indirect measurement technique.
    • Whenever dimensions are given in both feet and inches, you must convert them to either feet or inches before doing any calculations. Helpful Hint
    • Tyler wants to find the height of a telephone pole.
    • Tyler wants to find the height of a telephone pole. He measured the pole’s shadow and his own shadow and then made a diagram. What is the height h of the pole?
    • Example 1 Continued Step 1 Convert the measurements to inches. Step 2 Find similar triangles. Because the sun’s rays are parallel, A F. Therefore ∆ABC ~ ∆FGH by AA ~. AB = 7 ft 8 in. = (7 12) in. + 8 in. = 92 in. BC = 5 ft 9 in. = (5 12) in. + 9 in. = 69 in. FG = 38 ft 4 in. = (38 12) in. + 4 in. = 460 in.
    • Example 1 Continued Step 3 Find h. The height h of the pole is 345 inches, or 28 feet 9 inches. Corr. sides are proportional. Substitute 69 for BC, h for GH, 92 for AB, and 460 for FG. Cross Products Prop.92h = 69 460 Divide both sides by 92.h = 345
    • Volume ratios
    • The lateral areas of two similar cylinders are 50 cm2 and 18 cm2. The volume of the smaller cylinder is 54 cm3. Find the volume of the larger cylinder