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
<pre>
{{{drawing(200,2240/13,-1,5.5,-1,4.6, locate(0,0,X),locate(4.5,0,Y),
locate(4.5,4,Z), locate(2.3,0,45m), locate(4.7,1.9,36m), 

triangle(0,0, 4.5,0,  4.5,3.6)   )}}}

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 = &#8730;<span style="text-decoration: overline">3321</span>
 XZ = &#8730;<span style="text-decoration: overline">81·41</span>
 XZ = 9&#8730;<span style="text-decoration: overline">41</span>

{{{drawing(200,2240/13,-1,5.5,-1,4.6, locate(0,0,X),locate(4.5,0,Y),
locate(4.5,4,Z), locate(2.3,0,45m), locate(4.7,1.9,36m),
locate(1.1,2.3,9sqrt(41)), 

triangle(0,0, 4.5,0,  4.5,3.6)   )}}}

a) cos(Z) = {{{ADJACENT/HYPOTENUSE}}} = {{{36/(9sqrt(41))}}} = {{{4/(sqrt(41))}}} = {{{4sqrt(41)/41}}} 
b) measure of XY (That's given as 45m. Did you mean XZ? It's 9&#8730;<span style="text-decoration: overline">41</span>)
c) measure the angle of X (Find inverse tangent of {{{36/45}}} as 38.66°
d) tan(X) = {{{OPPOSITE/ADJACENT}}} = {{{36/45}}} = {{{4/5}}} 
e) sin(Z) = {{{OPPOSITE/HYPOTENUSE}}} = {{{45/(9sqrt(41))}}} = {{{5/(sqrt(41))}}} = {{{5sqrt(41)/41}}} 
f) tan(Z) = = {{{OPPOSITE/ADJACENT}}} = {{{45/36}}} = {{{5/4}}} 

Edwin</pre>