The diagonal of a rectangle is 8 inches long. It makes an angle of 22 with the length of the rectangle. 8 in
width
22°
length
What is the length of the rectangle to the nearest tenth?
5.7 in
3 in
O 7.4 in
3.2 in

d

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