The lengths of the two adjacent sides of parallelogram are 6 and 15. If the degree measure?

Question

Cont. - If the degree measure of an included angle is 60°, what is the lenght of the shorter diagnol of the parallelogram?

Answer 1

So this can be drawn as two equilateral triangles of side 6 (one up, one down), with the base of one connected to the vertex of the other with a segment of length 15-6 = 9

So the height of the parallelogram is 6*sqrt(3)/2, and the distance from the "height" line to the vertex is (1/2)*6 + 9 = 12.

So, short diagonal is hypotenuse of triangle with legs 3*sqrt(3) and 12.

L = sqrt(12^2 + 3*3^2) = sqrt(144+27) = sqrt(171)

Answer 2

You can use the law of cosine.

the lenght of the shorter diagnol
= sqrt[15^2+6^2-2(15)(6)cos(60)]
= sqrt(171)

Answer 3

d^2 = 6^2 + 15^2 - 2*6*15/2
d^2 = 36 + 225 - 90
d^2 = 171
d = √171 ≈ 13.076670 ≈ 13

(13^2 = 169)