Answer:
[tex]cos(V)=\frac{39}{89}=.44[/tex]
∠[tex]V=64.01[/tex]°
Step-by-step explanation:
[tex]sin(angle)=\frac{opposite}{hypotenuse}[/tex]
[tex]cos(angle)=\frac{adjacent}{hypotenuse}[/tex]
[tex]tan(angle)=\frac{opposite}{adjacent}[/tex]
- The cosine of an angle is equal to the side adjacent to the angle over the hypotenuse, the longest side.
[tex]cos(V)=\frac{39}{hypotenuse}[/tex]
- We need to find the hypotenuse of this triangle. This is relativly easy to do with a right triangle; we can just use the Pythagorean Theorem.
- Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex] where [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] are the 3 different sides of a right triangle.
[tex]a^2+b^2=c^2\\(39)^2+(80)^2=c^2\\1521+6400=c^2\\c=\sqrt{7921} \\c=89[/tex]
- Our hypotenuse is [tex]89[/tex]. Now we can finish solving for ∠[tex]V[/tex].
[tex]cos(V)=\frac{39}{89}\\V=cos^-^1(\frac{39}{89})\\[/tex]
∠[tex]V=64.01[/tex]°
