Answer:
Step-by-step explanation:
This is classic right triangle trig. W is an angle we are looking for. When looking for a missing angle on your calculator, you need the 2nd button and then either the sin, cos, or tan button as well, depending upon which trig ratio needs to used. We need to figure that out.
Opposite from angle W we have a side measuring 9. 15 is the hypotenuse. The trig ratio that relates the side opposite to the hypotenuse is the sin ratio. The sin of an angle is equal to the side opposite over the hypotenuse:
[tex]sinW=\frac{9}{15}[/tex]
Hit the 2nd button, then the sin button, and you will see on your calculator:
[tex]sin^{-1}([/tex]
After the open parenthesis enter in 9/15 and hit "enter" and you'll get your missing angle to be 36.9°. If you didn't get that exact angle, you are probably in radian mode and you'll need to change that.
As for finding x:
x is a side not an angle, so we won't need our 2nd button here. Look at the triangle. Angle W and the vertex angle of the right triangle on the right both have a single swish. That means that they have the same measure. We can use that to solve for x. The side measuring 9 is next to the angle in question so it's adjacent, and x is the hypotenuse. This will require the cos ratio to solve. The cos of an angle is equal to the side adjacent over the hypotenuse:
[tex]cos36.9=\frac{9}{x}[/tex]
Algebraically manipulate this by changing places of the cos36.9 and the x:
[tex]x=\frac{9}{cos36.9}[/tex] and get that
x = 11.3
