Question

Help find the missing lengths round to nearest tenth

Answer 1

Answer:

x = 20.8

y = 22.3

Step-by-step 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.

$tan 21=\frac{opposite}{adjacent} \\tan 21 =\frac{8}{x} \\0.384 =\frac{8}{x} \\0.384x =8 \\x=\frac{8}{0.384} \\x=20.84$

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

$sin 21=\frac{opposite}{hypotenuse} \\sin21 =\frac{8}{y} \\0.358 =\frac{8}{y} \\0.358y=8 \\y=\frac{8}{0.358} \\y=22.32$