Answer:
[tex]\tan(A) = \frac{3}{5}[/tex]
Step-by-step explanation:
Given
[tex]\sin(A) = \frac{3}{\sqrt {34}}[/tex]
[tex]0 \le A \le 90[/tex] --- First Quadrant
Required
Find tan(A)
The sin of an angle is:
[tex]\tan(A) = \frac{Opposite}{Hypotenuse}[/tex]
and
[tex]\sin(A) = \frac{3}{\sqrt {34}}[/tex]
By comparison:
[tex]Opposite = 3[/tex]
[tex]Hypotenuse = \sqrt{34[/tex]
So, the Adjacent is:
[tex]Hypotenuse^2 = Adjacent^2 + Opposite^2[/tex]
[tex](\sqrt{34})^2 = Adjacent^2 + 3^2[/tex]
[tex]34 = Adjacent^2 + 9[/tex]
Collect like terms
[tex]Adjacent^2 =34 - 9[/tex]
[tex]Adjacent^2 =25[/tex]
Take square roots
[tex]Adjacent =\sqrt{25[/tex]
[tex]Adjacent =5[/tex]
The tangent of an angle is:
[tex]\tan(A) = \frac{Opposite}{Adjacent}[/tex]
This gives:
[tex]\tan(A) = \frac{3}{5}[/tex]
