Length of Shorter Diagonal

**sharkman** · September 7th 2009, 05:55 AM

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}

**skeeter** · September 7th 2009, 06:51 AM

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 ...

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

**sharkman** · September 7th 2009, 07:06 AM

Originally Posted by skeeter

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

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

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

**skeeter** · September 7th 2009, 07:30 AM

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, $a$ using the known side ratios of a 30-60-90 triangle.

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

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.

**sharkman** · September 9th 2009, 08:51 AM

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, $a$ using the known side ratios of a 30-60-90 triangle.

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

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.

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Length of Shorter Diagonal

thanks but...

yes...

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