Answer:
1) x = 20. 8
2) x = 42.3
3) x = 13.0
4) x = 42.1
Step-by-step explanation:
1) Use Sine
(Sine = [tex]\frac{opposite}{hypothenuse}[/tex]) Sine 53 = [tex]\frac{x}{26}[/tex]
(sine of 53 is 0.80) 0.80 = [tex]\frac{x}{26}[/tex]
(multiply 26 on both sides) 0.80 x 26 = [tex]\frac{x}{26}[/tex] x 26
(solve) 20.8 = x
2) Use Tan
(Tan = [tex]\frac{opposite}{adjacent}[/tex]) Tan 78 = [tex]\frac{x}{9}[/tex]
(tan of 78 is 4.70) 4.70 = [tex]\frac{x}{9}[/tex]
(multiply 9 on both sides) 4.70 x 9 = [tex]\frac{x}{9}[/tex] x 9
(solve) 42.3 = x
3) Use Cosine
(Cosine = [tex]\frac{adjacent} {hypothenuse}[/tex]) Cos 22 = [tex]\frac{14}{x}[/tex]
(cos of 22 is 0.93) 0.93 = [tex]\frac{14}{x}[/tex]
(multiply 14 on both sides) 0.93 x 14 = [tex]\frac{14}{x}[/tex] x 14
(solve) 13.02 = x
(round to the nearest tenth) 13.02 = 13.0
4) Use tan
(Tan = [tex]\frac{opposite}{adjacent}[/tex]) Tan 39 = [tex]\frac{52}{x}[/tex]
(tan of 39 is 0.809) 0.809 = [tex]\frac{52}{x}[/tex]
(multiply 52 on both sides) 0.809 x 52 = [tex]\frac{52}{x}[/tex] x 52
(solve) 42.068 = x
(round to the nearest tenth) 42.068 = 42.1
