Question

A parallelogram has side lengths of 4 and 6 and an angle of measure 55°.

Answer 1

The Law of Cosines is a beautiful formula and a gateway to all sorts of wonders. 

This question asking for the length to the nearest whole number is pretty ugly.

A diagonal of a parallelogram makes two congruent triangles.   In this problem we're almost told we're interested in the diagonal opposite an A=55 degree angle, included between sides b=4 and c=6.

$a^2 = b^2 + c^2 - 2 b c \cos A$

We just plug in the numbers.

$a^2 = 4^2 + 6^2 - 2(4)(6) \cos 55^\circ$

$a^2 = 52 - 48 \cos 55^\circ$

That's the exact answer, its square anyway. Now we approximate.  

$\cos 55^\circ \approx .57$

$a^2 = 52 - 48(.57) = 24.6$

Taking the square root to the nearest integer, 

$a = 5$

Answer 2

Answer:

5 or b

Step-by-step explanation: