Question

Solve for x. round to the nearest hundredth if necessary.

Answer 1

11.47

Explanation:

Given

Two angles of 90 and 55 degrees

and a side of length 20

Finding third angle= 180-(90+55)

= 35

Finding x:

Using Law of Sines to find length of side x

x/sinX=y/SinY

x/sin35=20/sin90

x=20sin35

x=11.47 !

Answer 2

`x= 11.47`

Explanation:

By definition the cosine of an angle is the quotient between the side adjacent to the angle and the hypotenuse.

In other words:

`cos (\alpha) = (adjacent)/(hypotenuse)`

In this triangle the length of the side adjacent to the 55 degree angle is x, and the length of the hypotenuse is 20

So:

`cos(55\°) = (x)/(20)`

Now we solve the equation to find the value of x

`x = 20cos(55\°)`

Finally

`x= 11.47`