SOLUTION: Triangle XYZ is right angles at Y, XY is 45 m YZ is 36 m. Using the given measures find a) cos Z b) measure of XY c) measure the angle of X d) tan X e) sin Z f) tan Z

Algebra ->  Trigonometry-basics -> SOLUTION: Triangle XYZ is right angles at Y, XY is 45 m YZ is 36 m. Using the given measures find a) cos Z b) measure of XY c) measure the angle of X d) tan X e) sin Z f) tan Z      Log On


   



Question 684319: Triangle XYZ is right angles at Y, XY is 45 m YZ is 36 m. Using the given measures find
a) cos Z
b) measure of XY
c) measure the angle of X
d) tan X
e) sin Z
f) tan Z

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Triangle XYZ is right angles at Y, XY is 45 m YZ is 36 m. Using the given measures find
a) cos Z
b) measure of XY
c) measure the angle of X
d) tan X
e) sin Z
f) tan Z


First we find the hypotenuse XZ using the Pythagorean theorem

c² = a² + b²  with a = XY, b = YZ, and c = XZ

XZ² = XY² + YZ²
XZ² = 45² + 36²
XZ² = 2025 + 1296
XZ² = 3321
 XZ = √3321
 XZ = √81·41
 XZ = 9√41



a) cos(Z) = ADJACENT%2FHYPOTENUSE = 36%2F%289sqrt%2841%29%29 = 4%2F%28sqrt%2841%29%29 = 4sqrt%2841%29%2F41 
b) measure of XY (That's given as 45m. Did you mean XZ? It's 9√41)
c) measure the angle of X (Find inverse tangent of 36%2F45 as 38.66°
d) tan(X) = OPPOSITE%2FADJACENT = 36%2F45 = 4%2F5 
e) sin(Z) = OPPOSITE%2FHYPOTENUSE = 45%2F%289sqrt%2841%29%29 = 5%2F%28sqrt%2841%29%29 = 5sqrt%2841%29%2F41 
f) tan(Z) = = OPPOSITE%2FADJACENT = 45%2F36 = 5%2F4 

Edwin