Question

Find the value of each variable.​

Answer 1

Step-by-step explanation:

11)

x= 5

${y}^{2} = 2 \times {5}^{2} \\ {y}^{2} = 50 \\ y = 5 \sqrt{2}$

12)

$\tan(30 ) = \frac{9}{y} \\ y = \frac{9}{ \tan(30) } = 9 \sqrt{3} \\ {x}^{2} = {9}^{2} + {(9 \sqrt{3} )}^{2} \\ {x}^{2} = 324 \\ x = 18$

13)

$\sin(60) = \frac{x}{22} \\ x = 11 \sqrt{3} \\ \cos(60) = \frac{y}{22} \\ y = 11$

14)

${16}^{2} = {x}^{2} + {y}^{2} \\ x = y \\ {16}^{2} = 2 {x}^{2} \\ x = 8 \sqrt{2} \\ y = 8 \sqrt{2}$

15)

$\tan(30) = \frac{x}{42} \\ x = 14 \sqrt{3} \\ \cos(30) = \frac{42}{y} \\ y = \frac{42}{ \cos(30) } \\ y = 28 \sqrt{3}$

16)

${(19 \sqrt{2}) }^{2} = {x}^{2} + {y}^{2} \\ x = y \\ 722 = 2 {x}^{2} \\ {x}^{2} = 361 \\ x = 19 \\ y = 19$