Answer:
Part 1) The measure of x is 23°
Part 2) The value of y is [tex]y=5\ units[/tex]
Part 3) The value of z is [tex]z=12\ units[/tex]
Step-by-step explanation:
step 1
Find the value of x
we know that
[tex]x+67\°=90\°[/tex] ------> by complementary angles
[tex]x=90\°-67\°=23\°[/tex]
step 2
Find the value of y
In the right triangle of the figure
[tex]cos(67\°)=\frac{y}{13}[/tex] -----> adjacent side angle of 67 degrees divided by the hypotenuse
[tex]y=(13)cos(67\°)=5\ units[/tex]
step 3
Find the value of z
In the right triangle of the figure
[tex]sin(67\°)=\frac{z}{13}[/tex] -----> opposite side angle of 67 degrees divided by the hypotenuse
[tex]z=(13)sin(67\°)=12\ units[/tex]
