Question 1025094: A triangular parcel of land with points M,K,L was to be fenced.No data for the lengths of sides MK and KL are available as shown in the figure below. (the link-the picture.) ---> https://www.pinterest.com/pin/467741111280793052/
(if you cannot click the illustration/picture,pleae copy+paste it.thanks~)
please I really need help. :)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! not sure what they are asking as the picture doesn't show that.
what i see, however, indicates that you would use the law of sines to find the lengths of the corresponding sides.
your triangle is MKL
you are given that:
angle M is 83 degrees.
angle K is 52 degrees
since the sum of the angles of a triangle is equal to 180 degrees, then you can determine that angle L is equal to 180 - 84 - 52 = 45 degrees.
you are given that side ML is equal to 150.
you would use the law of sines to determine the length of the other sides.
the law of sines says that the sine of the angle divided by its opposite side is the same for all angles and sides of the triangle.
this means that:
sine of angle M / KL is equal to sine of angle K / ML is equal to sine of angle L / MK
you know that the opposite side to angle K is side ML.
you have determined all the angles.
from that, you get the following equations.
sine(M) / KL = sine(K) / 150 = sine(L) / MK
replace the angles with their measures and you get:
sine(52) / KL = sine(84) / 150 = sine(45) / MK
solve each equation separately.
start with:
sine(52) / KL = sine(84) / 150.
solve for KL to get KL = (sine(52) * 150) / sine(84).
you will get KL = 119.09
continue with:
sine(83) / 150 = sine(45) / MK
solve for MK to get MK = (sine(45) * 150) / sine(83)
you will get MK = 106.87
you now have the length of all the sides.
the perimeter of the triangle is the sum of the lengths.
the length are 150 + 119.09 + 106.87
the perimeter is therefore equal to 375.96.
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