Trigonometry Question

Question

In  Triangle(XYZ) , x = 12",   y = 14",   and z = 16". Find m/ Z and m/ X.

m/ Z = Answer (Round to the nearest whole degree)

m/ X = Answer (Round to the nearest whole degree)

Answer 1

You the cosine law for these:

m/Z:

z² = x² + y² -2xycos(Z)

cos(Z) = (256 - 144 - 196)/(2(12)(14) = -84/-336 = 0.25

Z = cos^-1(0.25) ≈ 76 degrees = m/Z

m/X:

x² = y² + z² - 2yzcos(X)

cos(X) = (144 - 256 - 196)/(2(14)(16)) = -308/-448 = 0.6875

X = cos^-1(0.6875) ≈ 47 degrees

By the way Y = 180 - 47 - 76 = 57 degrees