SOLUTION: Hello my teacher gave my class a worksheet with this problem: The lengths of two sides of a parallelogram are 6 inches and 10 inches and the angle between them measures 41 degr

Algebra ->  Trigonometry-basics -> SOLUTION: Hello my teacher gave my class a worksheet with this problem: The lengths of two sides of a parallelogram are 6 inches and 10 inches and the angle between them measures 41 degr      Log On


   

Question 278282: Hello my teacher gave my class a worksheet with this problem:
The lengths of two sides of a parallelogram are 6 inches and 10 inches and the angle between them measures 41 degrees. What is the length of the altitude on the long side?
Thanks for any help.

Found 2 solutions by mananth, ikleyn:
Answer by mananth(16949) About Me  (Show Source):
You can put this solution on YOUR website!
The lengths of two sides of a parallelogram are 6 inches and 10 inches and the angle between them measures 41 degrees. What is the length of the altitude on the long side?
let ABCD be the parellogram . ab =6 and bc =10 the angle between them = 41 deg.
Extend DA to P and join it from b
We have to find length length DP. DP = DA + AP
we have to find length AP in triangle APB
AP / AB = cos 41
Cos 41=0.98
AP = 0.98 * AB
AP= 0.98*6
AP=5.88
The length of altitude = 5.88 +10 = 15.88 inches


Answer by ikleyn(53742) About Me  (Show Source):
You can put this solution on YOUR website!
.
Hello, my teacher gave my class a worksheet with this problem:
The lengths of two sides of a parallelogram are 6 inches and 10 inches and the angle between them measures 41 degrees.
What is the length of the altitude on the long side?
Thanks for any help.
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        This is a nice problem, and I will show you a remarkable method to solve it.

        The solution and the answer in the post by @mananth are fatally incorrect.
        It is fatally incorrect, because both the guiding idea (the conception) and calculations are wrong. 


The idea is to use two different formulas for the area of the parallelogram.


One formula for the area of the parallelogram is

    area = a*b*sin(41°).     (1)  


It says that the area of the parallelogram is the product of its two adjacent sides by the sine of the angle between them.
Another formula for the area of the parallelogram is

    area = a*h.             (2)


It says that the area of the parallelogram is the product of its base (one of the two adjacent sides)
by the altitude of the parallelogram h.


Thus we equate right sides in formulas (1) and (2)

    a*b*sin(41°) = a*h.


We then cancel the common factor 'a', and we get

    h = b*sin(41°).    (3)


Now from (3) we get the value of 'h'

    h = b*sin(41°) = 6*0.65605902899 = 3.936 inches  (rounded).

At this point, the problem is solved completely and correctly,
and you learned a new method for this problem.