Question

Last one, use trigonometry to help you solve for y given that one side is 4 and there is an angle of 50 degrees.

Answer 1

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.

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

`\cos(50) = (4)/(y)`

`\cos(50) * y = 4`

`y = (4)/( \cos(50) )`

`y = 6.22`

2.) Use Law of Sines:

Solve for the last angle inside the triangle first.

`180 - (50 + 90) = 40`

Then use the angle you found (40°) in the equation.

`(4)/( \sin(40) ) = (y)/( \sin(90) )`

`(4)/( \sin(40) ) * \sin(90) = y`

`y = 6.22`