Prove that δabc and δedc are similar.

the blanked out numbers are 15 and 12

a) ∠dce is congruent to ∠bca by the vertical angles theorem and 15 over 5 equals 12 over 4 shows the corresponding sides are proportional; therefore, δabc ~ δedc by the sas similarity postulate.

b)∠dce is congruent to ∠cba by the vertical angles theorem and 15 over 5 equals 12 over 4 shows the corresponding sides are proportional; therefore, δabc ~ δedc by the sss similarity postulate.

Nthe opening scene of the movie raiders of the lost ark, indiana jones replaces a golden statue with a bag of sand. the platform on which the statue is placed is designed to detect the mass of the statue. if the bag of sand has a different mass than the statue, then a mechanism triggers and destruction ensues. the density of gold is about 20\text{ g/cm}^320 g/cm 3 20, space, g, slash, c, m, start superscript, 3, end superscript. the density of sand can be estimated at 2.5\text{ g/cm}^32.5 g/cm 3 2, point, 5, space, g, slash, c, m, start superscript, 3, end superscript. the gold statue can be modeled as a cylinder with height 25\text{ cm}25 cm25, space, c, m and radius 8\text{ cm}8 cm8, space, c, m. in terms of \piπpi, what is the mass of sand indiana jones needs to avoid triggering the mechanism?