Answer:
Step-by-step explanation:
Do you know SOHCAHTOA
Sin = opposite/hypotenuse
Cosine = adjacent/hypotenuse
Tangent = opposite/adjacent
#1
We have to find cos(x) = adjacent/hypotenuse
[tex]cos(x) = adj/hyp\\=\frac{24}{26} = \frac{12}{13}[/tex]
#2:
We are given an angle of 30 degrees and an opposite side of 15
We need to find the adjacent side, so we can use Tangent
[tex]tan(30) = \frac{15}{adj}[/tex]
[tex]adj = \frac{15}{tan(30)} = 25.98 = 26[/tex]
#3
We are given an angle and an opposite side and we have to solve for hypotenuse.
We can use sin
[tex]sin(43) = \frac{16}{x} \\x = \frac{16}{sin(43)} = 23.46 = 23.5[/tex]
#4:
We are given two sides, we have to find the angle. We are given an opposite side and an adjacent side, so we can use arctangent ([tex]tan^-1(x)[/tex], but not 1/tan(x))
[tex]tan(x) = \frac{36}{19} \\arctan(36/19) = x\\x = 62.1759[/tex]
#5
We are given an opposite side and the hypotenuse, we can use sin
[tex]sin(x) = \frac{19}{28}\\x = arcsin(19/28) = 42.73 = 43[/tex]