Step-by-step explanation:
11)
x= 5
[tex] {y}^{2} = 2 \times {5}^{2} \\ {y}^{2} = 50 \\ y = 5 \sqrt{2} [/tex]
12)
[tex] \tan(30 ) = \frac{9}{y} \\ y = \frac{9}{ \tan(30) } = 9 \sqrt{3} \\ {x}^{2} = {9}^{2} + {(9 \sqrt{3} )}^{2} \\ {x}^{2} = 324 \\ x = 18[/tex]
13)
[tex] \sin(60) = \frac{x}{22} \\ x = 11 \sqrt{3} \\ \cos(60) = \frac{y}{22} \\ y = 11[/tex]
14)
[tex] {16}^{2} = {x}^{2} + {y}^{2} \\ x = y \\ {16}^{2} = 2 {x}^{2} \\ x = 8 \sqrt{2} \\ y = 8 \sqrt{2} [/tex]
15)
[tex] \tan(30) = \frac{x}{42} \\ x = 14 \sqrt{3} \\ \cos(30) = \frac{42}{y} \\ y = \frac{42}{ \cos(30) } \\ y = 28 \sqrt{3} [/tex]
16)
[tex] {(19 \sqrt{2}) }^{2} = {x}^{2} + {y}^{2} \\ x = y \\ 722 = 2 {x}^{2} \\ {x}^{2} = 361 \\ x = 19 \\ y = 19[/tex]
