A marching band routine requires a tuba player to begin at the 50-yard line of a football field and march perpendicular to the 40-yard line. He then makes a 30 degree turn and marches at a diagonal back to the 50-yard line. Once he reaches the 50-yard line, he must march forward until he reaches his original starting position. If the tuba player travels 18 inches with each marching pace, how many paces must he take to complete the routine? Round to the nearest pace. ? paces

eve and marks ratios are equivalent

step-by-step explanation:

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

1/3 + 1/3 ≠ 2/6 because 1/3 alone = 2/6  

step by step explanation:

1/3 + 1/3 = 2/3       2/3=4/6

the answer is 40.

proof: