This is more tedious than difficult......!!!......it's asking for the perimeter
Starting with the triangle on the right.....the two equal sides = 2(2/sqrt(3))(1.5) cm = 6/sqrt(3) = 2sqrt(3) = A
And we need to find the other side [ the base] for a calculation in the next triangle on the left....using the Law of Sines, we can calculate 1/2 the base length = x
[ x] / sin(30) = 1.5 / sin(60)
2x = [1.5 *2 ] / sqrt(3)
x = 1.5/[sqrt(3)] and the base is twice this 3/sqrt(3) = sqrt(3)
In the next triangle to the left, the missing angle = 35 degrees and we can find the base of this triangle using the Law of Sines
base / sin 90 = [sqrt(3)] /sin(35)
So the base = [sqrt(3)]/sin(35) = B
And we need to find the length of the remaining side of this triangle - the side with the two hash marks = for a calculation in the next triangle to the top left.......we'll call this missing side x, again
And with the Law of Sines, we have
x/ sin55 = [sqrt(3)]/ sin(35) = sin(55)*[sqrt(3)]/ sin(35) = C
And we can find the remaining top perimeter as
x/ sin(110) = [sin(55)*[sqrt(3)]/ [sin(35)]/ [sin(35)]
So....the remaining top perimeter = [sin(110)][sin(55)*[sqrt(3)]/ [sin(35)]^2 = D
And we can find the leftmost side of the recatangle on the left as :
x /sin(35) = sin(55)*[sqrt(3)]/ [sin(35)]
So this side = sin(55)*[sqrt(3)] = E
And the remaining length will be the bottom of the rectangle on the left......and this is just 1/2 the length of D = (1/2)[sin(110)][sin(55)*[sqrt(3)]/ [sin(35)]^2 = F
So...the total perimemter=
A + B + C + D + E + F =
[2sqrt(3) + [sqrt(3)]/sin(35) + sin(55)*[sqrt(3)]/ sin(35) + [sin(110)][sin(55)*[sqrt(3)]/ [sin(35)]^2 +
sin(55)*[sqrt(3)] + (1/2)[sin(110)][sin(55)*[sqrt(3)]/ [sin(35)]^2] cm
So the total perimeter = about 16.369 cm
P.S......you should check my math......this one was drawn out and I may have made a mistake someplace....!!!!
