SOLUTION: One side and the altitude of a rhombus measure 120 m and 90 m respectively. a) Find the area of the rhombus. b) Find the smaller interior angle of the rhombus. c) Find the lengt

Algebra ->  Polygons -> SOLUTION: One side and the altitude of a rhombus measure 120 m and 90 m respectively. a) Find the area of the rhombus. b) Find the smaller interior angle of the rhombus. c) Find the lengt      Log On


   

Question 1185591: One side and the altitude of a rhombus measure 120 m and 90 m respectively.
a) Find the area of the rhombus.
b) Find the smaller interior angle of the rhombus.
c) Find the length of the shorter diagonal.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a) Just like any parallelogram, the area will be base x height = 120+%2A+90+m%5E2+=+%2210%2C800%22+m%5E2.

b) The smaller interior angle of the rhombus can be obtained from sin%28theta%29+=+90%2F120+=+3%2F4. This would give 48.59%5E0, to 2 d.p.

c) The length of the shorter diagonal can be obtained from getting the value of 2alpha from alpha%2F120+=+sin%28theta%2F2%29+=+sin%2848.59%2F2%29.
Therefore the length of the shorter diagonal is 98.74 meters, to 2 d.p.