Answer:
The answer to your question is y = 6.54, w = 11.31
Step-by-step explanation:
Process
1.- Find the length of the opposite side of the left triangle
sin Ф = Opposite side/hypotenuse
Ф = 45°
hypotenuse = 8
-Solve for Opposite side
Opposite side = hypotenuse x sin Ф
-Simplify
Opposite side = 8 sin45
-Result
Opposite side = 5.66
2.- Find w
-To find w use the trigonometric function sine
sin Ф = Opposite side / hypotenuse (w)
-Solve for w
w = Opposite side/sin Ф
-Substitution
w = 5.66/ sin 30
-Result
w = 11.31
3.- Find y
-To find y use the trigonometric function cosine
cos Ф = Opposite side / Adjacent side (y)
-Solve for y
y = Opposite side / cos Ф
-Substitution
y = 5.66 / cos 30
-Result
y = 6.54
