Question 1132824
xyz is the right triangle.
the 90 degree angle is at y.
xy = yz so this is an isosceles right triangle.
the hypotenuse of this right triangle is xz which is equal to sqrt (25 + 25) = sqrt(50).


the trigonometric functions are:


cos(z) = yz/xz = 5/sqrt(50)
tan(z) = xy/yz = 5/5 = 1
csc(z) = 1/sin(z) = 1/(xy/xz) = 1/(5/sqrt(50)) = sqrt(50)/5.
sec(z) = 1/cos(z) = 1/(yz/xz) = 1/(5/sqrt(50) = sqrt(50)/5.


since this is an isosceles right triangle, angle z must be equal to 45 degrees and also angle x must be equal to 45 degrees as well.


you can use your calculator to confirm that:


cos(45) = .7071067812 and 5/sqrt(50) = the same.
likewise, tan(45) = 1
likewise csc(45) = 1 / sin(45) = 1.414213562 and sqrt(50)/5 = the same.
likewise sec(45) = 1 / COS(45) = 1.414213562 and sqrt(50)/5 = the same.