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In a parallelogram, two adjacent sides measure 20 cm and 27 cm. The shorter diagonal is 23 cm. Determine, to the nearest degree, the measure of the larger angles in the parallelogram.

Sagot :

If two adjacent sides of parallelogram are 20 cm and 27 cm and the shorter diagonal is 23 cm then the measure of larger angles in the parallelogram is 123.75°.

Given Two adjacent sides are 20 cm and 27 cm. The shorter diagonal is 23 cm. and we need to find the measure of larger angle.

From law of cosines

[tex]c^{2} =a^{2} +b^{2} -2abcos d[/tex]

where c is the opposite side of angle, a and b are other sides and d is the angle.

[tex]23^{2} =20^{2} +27^{2} -2*20*27cos d[/tex]

where 23 is the length of shorter diagonal

529=400+729 - 1080 cos d

1080 cos d=600

cos d=600/1080

cos d=0.55

d=[tex]cos^{-}[/tex]0.55

d=56.25°

Adjacent angle=180-56.25

=123.75°

Largest angle=123.75°.

Hence the larger angle of parallelogram having sides 20 and 27cm is 123.75°.

Learn more about parallelogram at https://brainly.com/question/970600

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