Question

The diagonals of a rectangle have length 12 and intersect in a 40 degree angle. Find the length and width rounded to the nearest tenth.

Answer 1

Length is 7.7 and width is 9.2

Explanation:

The length and width of the rectangle will be the y and x coordinate of the diagonal line at angle of 40 degrees

Length L = dsin theta

Width W = d coos theta

d is the length of the diagonal

Given

d = 12

theta = 40°

Substitute

Length = 12sin40°

Length = 12(0.6428)

Length = 7.7135

Length ≈ 7.7

Width = 12cos 40

Width = 12(0.7660)

Width = 9.192

Width = 9.2

Hence the length is 7.7 and width is 9.2