the side length of a parallelogram are 4in and 12in.The area of the parallelogram is 24.What are the values for the two angles of the parallelogram.

Question

the side length of a parallelogram are 4in and 12in.The area of the parallelogram is 24.What are the values for the two angles of the parallelogram.Steps will really help me solve similar problems later on.Thank you

Answer 1

Hey Ace,

in parallelogram we have an obtuse angle which is >180 and an acute <180.

let's recall what do we know about the area of a parallelgram

Area=HeightxBase

base we have it is 12 in

height is what we are missing

 but we have the area

so 24=12h

h=2 in

but the question is why do we need the h anyway? what is the point

now remember we are also given the other side of parallelogram 4 in

we construction a height within a parallelogram you are making a right triangle

so doesnt that mean we can use trigonometry? yes!

height would be in this case the opposite and the side length 4in would be the hypotenuse (construction would show this)

so using sin we can find one angle of this parallelgram Call the angle A

sin(A)=2/4=1/2

so A=30 degrees

now there is one fact in a parallelogram the sum of all angles is 360

then we have 2(30)+2y=360

y being the other missing angle

why 2 (because in parallelogram opposing angles are congruent so we two of each congruent angles)

2y=300

y=150

so x=30 and y=150

those are the angles desired

hope that helps