SOLUTION: the following problems. Show solutions and illustrate the given.
1. A parallelogram has sides 15 cm and 25 cm and their included angle is
740
.
I. Find its area.
II. Find the
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Question 1201469: the following problems. Show solutions and illustrate the given.
1. A parallelogram has sides 15 cm and 25 cm and their included angle is
740
.
I. Find its area.
II. Find the lengths of the diagonals.
III. Find the angle of intersection between diagonals.
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
to find the area of parallelogram with 2 sides and an angle use formula
Area = ab sin
Side 1 15 cm
side 2 25 cm
included angle =74 deg
A = 15 * 25 * sin 74 degrees
=360.47 cm^2
To find the third side of a triangle ( Here diagonal of parallelogram) given two sides and an angle. You use the cosine formula. If the three sides of the triangle are a, b and c and the angle between a and b is C, then c² = a² + b² - 2ab×cos C.
c = sqrt(15^2+25^2 - 2*15*25*cos 74 degrees)
c=25.36 cm
Sum of adjacent angles of parallelogram are supplementary
The other angle is 180-74 = 106 deg
Apply same formuala to get the other diagonal
32.507 cm
The diagonals bisect each other. So we can find the angle using the above formula. we can find the angle
.
25
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