Answer:
The answer to your question is x = [tex]7\sqrt{2}[/tex] and y = [tex]14\sqrt{3}[/tex]
Step-by-step explanation:
To find x and y use trigonometric functions
- Find x
To find x use the trigonometric function cosine
cosine Ф = adjacent side/hypotenuse
- Solve for adjacent side (x)
x = hypotenuse x cos Ф
- Substitution
x = 14[tex]\sqrt{2}[/tex] cos 60
Simplification
x = 14[tex]\sqrt{2}[/tex] (0.5)
x = 7[tex]\sqrt{2}[/tex]
- Find y
-Find the length of the opposite side of the small triangle
Opposite side = sine Ф x hypotenuse
Opposite side = 14[tex]\sqrt{2}[/tex] x sin 60
Opposte side = 14[tex]\sqrt{2}[/tex] ([tex]\sqrt{3}[/tex]/2)
Opposite side = 7[tex]\sqrt{6}[/tex]
- Find the length of y
y = Opposite side/sin Ф
y = [tex]7\sqrt{6}[/tex] / [tex]\sqrt{2} /2[/tex]
y = 14[tex]\sqrt{3}[/tex]
