Question

Find the values of XYNZ to the nearest integer

Answer 1

Part 1) The measure of x is 23°

Part 2) The value of y is
`y=5\ units`

Part 3) The value of z is
`z=12\ units`

Explanation:

step 1

Find the value of x

we know that

`x+67\°=90\°` ------> by complementary angles

`x=90\°-67\°=23\°`

step 2

Find the value of y

In the right triangle of the figure

`cos(67\°)=(y)/(13)` -----> adjacent side angle of 67 degrees divided by the hypotenuse

`y=(13)cos(67\°)=5\ units`

step 3

Find the value of z

In the right triangle of the figure

`sin(67\°)=(z)/(13)` -----> opposite side angle of 67 degrees divided by the hypotenuse

`z=(13)sin(67\°)=12\ units`