Answer:
[tex]x = 11.4[/tex]
Step-by-step explanation:
So there are ways to find a missing side of a triangle.
- Pythagorean Theorem
- Law of Sines
- Law of Cosines
- Sine,Tangent, or Cosine Function.
I'll explain when we use them,
- We use pythagorean theorem if we have a right angle and know at least two sides of a triangle. Since we dont know two sides, we are not going to use that.
- We use law of sines if we know a given angle and a side opposite of that angle and a side or angle opposite of the angle or side we are trying to find
- If we apply the triangle interior theorem, we can use law of sines. Since 11 and 44 degrees are opposite sides, and x and the missing angle which is 46 is opposite side and angle as well.
- We use law of Cosines if we know two sides and a angle between them. We have a missing side so we cant use law of Cosines.
- Since we are trying to find side measures, sometimes it isn't advised to use SOHCAHTOA.
- So let use law of sines.
[tex] \frac{11}{ \sin(44) } = \frac{x}{ \sin(46) } [/tex]
[tex] \frac{11}{ \sin(44) } \times \sin(46) = x [/tex]
[tex]x = 11.4[/tex]
