The lengths of two adjacent sides of a parallelogram are 6 and 15. If the degree measure of the included angle is 60, what is the length of the shorter diagonal of the parallelogram?

(a) sqrt{171}

(b) sqrt{148}

(c) sqrt{153}

(d) sqrt{261}

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- Sep 7th 2009, 05:55 AMsharkmanLength of Shorter Diagonal
The lengths of two adjacent sides of a parallelogram are 6 and 15. If the degree measure of the included angle is 60, what is the length of the shorter diagonal of the parallelogram?

(a) sqrt{171}

(b) sqrt{148}

(c) sqrt{153}

(d) sqrt{261}

- Sep 7th 2009, 06:51 AMskeeter
- Sep 7th 2009, 07:06 AMsharkmanthanks but...
- Sep 7th 2009, 07:30 AMskeeter
draw in the altitude from the end of the side of length 6 perpendicular to the side of length 15 ... a 30-60-90 triangle is formed with hypotenuse length 6.

determine the length of the altitude, $\displaystyle a$ using the known side ratios of a 30-60-90 triangle.

another right triangle is formed with legs of length "$\displaystyle a$" and $\displaystyle b = 12$.

the hypotenuse of that right triangle is the short diagonal ... use Pythagoras to find its length.

next time, please be sure to include all information about a problem, especially what methods can be used to solve it. - Sep 9th 2009, 08:51 AMsharkmanyes...