SOLUTION: A side and the altitude of a rhombus measure 120m and 90m respectively. Find the smaller interior angle of the rhombus.

Algebra ->  Parallelograms -> SOLUTION: A side and the altitude of a rhombus measure 120m and 90m respectively. Find the smaller interior angle of the rhombus.      Log On


   

Question 1143886: A side and the altitude of a rhombus measure 120m and 90m respectively.
Find the smaller interior angle of the rhombus.
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let  " a "  be the smaller interior angle of the rhombus (exactly the value under the problem's question).


Then  sin(a) = 90%2F120 = 3%2F4.


Hence,  a = arcsin(3/4).      ANSWER


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
see my worksheet below.
additional comments below the worksheet.

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reference on altitude of a rhombus can be found at https://www.mathopenref.com/rhombus.html#targetText=The%20altitude%20of%20a%20rhombus,may%20have%20to%20be%20extended).
reference on properties of a rhombus can be found at https://www.mbacrystalball.com/blog/2015/11/13/quadrilaterals-properties-parallelograms-trapezium-rhombus/

from my worksheet, DE is the altitude of rhombux ABCD.

\right triangle EAD is formed by the altitude and the closest side of the rhombus.

DE = 90 mm
AD = 120 mm

cos(EDA) = 90/120.

angle (EDA) = arccos(90/120) = 41.40962211 degrees = angle x in the diagram.

angle y in the diagram is complementary to angle x, since angle x + y = 90 degrees.

angle y is the smaller of the interior angles of rhombus ABCD.

angle y is equal to 90 minus angle x = 48.59037789 degrees.

that should be your answer as best i can determine.