Answer:
sin J = [tex]\frac{15}{29}[/tex]
cos J = [tex]\frac{21}{29}[/tex]
tan J = [tex]\frac{5}{7}[/tex]
x = 14.6
Step-by-step explanation:
1st pic:
1st, find the missing side lenght:
[tex]a^{2} = c^{2} - b^{2}[/tex]
[tex]a^{2} = 58^{2} - 42^{2}[/tex]
[tex]a^{2} = 3364 - 1764[/tex]
[tex]\sqrt{a^{2}} = \sqrt{1600}[/tex]
a = 40
sin = [tex]\frac{opposite}{hypothenuse}[/tex] ⇒ [tex]sin J = \frac{30}{58} = \frac{15}{29}[/tex]
cos = [tex]\frac{adjacent}{hypothenuse}[/tex] ⇒ [tex]cosJ = \frac{42}{58} = \frac{21}{29}[/tex]
tan = [tex]\frac{opposite}{adjacent}[/tex] ⇒[tex]tanJ = \frac{30}{42} = \frac{5}{7}[/tex]
2nd pic:
use sine:
sin = [tex]\frac{opposite}{hypothenuse}[/tex]
sine 59 = [tex]\frac{x}{17}[/tex]
sine of 59 is 0.857:
0.857 = [tex]\frac{x}{17}[/tex]
multiply 17 on both sides:
0.857 x 17 = [tex]\frac{x}{17}[/tex] x 17
14.569 = x
round to the nearest tenth:
14.569 = 14.6
