Answer:
y = 6.22
You can solve this in two ways.
1.) Use SOH CAH TOA:
I typically start off by labeling the sides of the triangle with H (hypotenuse), O (opposite), and A (adjacent). Because I need to figure out what y is when given an angle and 4, I will use CAH, or cosine.
[tex] \cos(angle) = \frac{adjacent}{hypotenuse} [/tex]
[tex] \cos(50) = \frac{4}{y} [/tex]
[tex] \cos(50) \times y = 4[/tex]
[tex]y = \frac{4}{ \cos(50) } [/tex]
[tex]y = 6.22[/tex]
2.) Use Law of Sines:
Solve for the last angle inside the triangle first.
[tex]180 - (50 + 90) = 40[/tex]
Then use the angle you found (40°) in the equation.
[tex] \frac{4}{ \sin(40) } = \frac{y}{ \sin(90) } [/tex]
[tex] \frac{4}{ \sin(40) } \times \sin(90) = y[/tex]
[tex]y = 6.22[/tex]
