Asked by sue
Trigonometry - determine the area of a parallelogram in which 2 sides are 10 and 13 and the angle between them is 55
Answers
Answered by
Reiny
the area of the parallelogram
= (1/2)(10+13)h , where h is the vertical distance between the parallel sides.
Since the value of h is constant between the 2 parallels
let's slide the longer side so that one end is vertically opposite the end of the shorter side
We can now construct a rectangle with a triangle at one end.
height of triangle = h
base of triangle = 3
base angle = 55°
tan 55 = h/3
h = 3 tan 55
area of ||gm = (1/2)(10+13)(3 tan 55°)
= ....
you do the button-pushing
= (1/2)(10+13)h , where h is the vertical distance between the parallel sides.
Since the value of h is constant between the 2 parallels
let's slide the longer side so that one end is vertically opposite the end of the shorter side
We can now construct a rectangle with a triangle at one end.
height of triangle = h
base of triangle = 3
base angle = 55°
tan 55 = h/3
h = 3 tan 55
area of ||gm = (1/2)(10+13)(3 tan 55°)
= ....
you do the button-pushing
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