Answer: 150mm
Step-by-step explanation:
Take the two adjecent sides of the triangle to be x and y and X is the angle opposite the side, x.
From the trigonometric identities for a right-angled triangle, it is known that
x=170sin X and;
y=170cos X
Thus the perimeter of the triangle is given by
170sin X + 170cos X + 170 = 400
170(sin X + cos X) = 400 - 170
170(sin X + cos X) = 230
sin X + cos X = 230/170 = 1.3529
Squaring both sides hence,
sin^2(X) + 2sin X.cos X + cos^2(X) = 1.8304
Recall that sin^2(X) + cos^2(X) = 1 and 2sin X.cos X = sin 2X.
Thus, the former expression gives;
1 + sin 2X = 1.8304
sin 2X = 0.8304
2X = arcsin (0.8304)
2X = 56.14° or (180 - 56.14)° = 56.14° or 123.86° for X existing within a triangle.
X = 56.14/2 or 123.86/2
X = 28.07° or 61.93°
Thus the two adjacent sides are ;
x = 170 sin (28.07) = 80mm
y = 170 cos (28.07) = 150mm
Using the value of 61.93° as X would give the same values but interchanged for x and y.
I hope you find this useful.
