Answer:
The answer to your question is below
Step-by-step explanation:
1) Find x
-Use trigonometric functions
sinФ = x / 10√3
-Solve for x
x = 10√3 x sin 30
-simplification
x = 10√3 x (1/2)
x = 5√3
-Calculate y
cos Ф = y/10√3
-solve for y
y = 10√3 x cos 30
-Simplification
y = 10√3 (√3/2)
-result
y = 10(3)/2
y = 15
2.-
sin Ф = x/15
-solve for x
x = 15 sin 45
-simplify
x = 15(√2)/2
-result
x = 15√2 / 2
3.- sin Ф = y/7
-solve for y
y = 7 sin 45
-simplify
y = 7 (√2)/2
-result
y = 7√2 / 2
-Calculate x
tanФ = 7√2/2 / x
-solve for x
x = 7/2√2 / tan 60
-simplify
x = 7/2√2 / √3
-result
x = 7√6/ 6
4.-
-Calculate the length of the right triangle
tan Ф = 11√2 / x
-solve for x
x = 11√2 / tan Ф
-substitution
x = 11√2 / 1
-result
x = 11√2
-Calculate b
b = 8√2 + 11√2
b = 19√2
-Calculate a
sinФ = 11√2 / a
-solve for a
a = 11√2 / sin 45
-simplification
a = 11√2 / √2/2
-result
a = 22
