Question

Help find the missing lengths round to nearest tenth

Answer 1

x = 20.8

y = 22.3

Explanation:

• Theta is 21 degrees

• x is the adjacent side
• 8 is the opposite side
• y is the hypothenuse

SOH - CAH - TOA

Since the opposite side is given and we need to find the length of the adjacent side, we can use tangent to solve for x.

`tan 21=(opposite)/(adjacent) \\tan 21 =(8)/(x) \\0.384 =(8)/(x) \\0.384x =8 \\x=(8)/(0.384) \\x=20.84`

Since the opposite side is given and we need to find the length of the hypotenuse, we can use sine to solve for y.

`sin 21=(opposite)/(hypotenuse) \\sin21 =(8)/(y) \\0.358 =(8)/(y) \\0.358y=8 \\y=(8)/(0.358) \\y=22.32`