# Length of Shorter Diagonal

• Sep 7th 2009, 05:55 AM
sharkman
Length 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 AM
skeeter
Quote:

Originally Posted by sharkman
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}

make a sketch and use the law of cosines ...

$\displaystyle a=\sqrt{b^2+c^2-2bc\cos{A}}$
• Sep 7th 2009, 07:06 AM
sharkman
thanks but...
Quote:

Originally Posted by skeeter
make a sketch and use the law of cosines ...

$\displaystyle a=\sqrt{b^2+c^2-2bc\cos{A}}$

Thank you but this question comes from a chapter on special right triangles. There is no mention of trig in that chapter at all.
• Sep 7th 2009, 07:30 AM
skeeter
Quote:

Originally Posted by sharkman
Thank you but this question comes from a chapter on special right triangles. There is no mention of trig in that chapter at all.

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 AM
sharkman
yes...
Quote:

Originally Posted by skeeter
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.

Exactly what I needed.