Step-by-step explanation:
003:
To solve this, we'll be using the Pythagorean theorem, [tex]a^2+b^2=c^2[/tex]
[tex]a^2+8^2=15^2\\a^2+64=225\\a^2=161\\a = \sqrt{161}[/tex]
004:
For the next couple questions we'll be using a fun rule called SOHCAHTOA, which stands for Sin (Opposite/Hypotenuse) Cos (Adjacent/Hypotenuse) Tan (Opposite/Adjacent). From this we can see that Tan θ is 8/[tex]\sqrt{161}[/tex].
005:
From this rule again, we can tell that sin Ф (Opposite/Hypotenuse) is going to be [tex]\sqrt{161}[/tex]/15.
Answer:
003: [tex]\sqrt{161}[/tex]
004: 8/[tex]\sqrt{161}[/tex]
005: [tex]\sqrt{161}[/tex]/15
