Answer:
Tan C = 3/4
Step-by-step explanation:
Given-
∠ A = 90°, sin C = 3 / 5
METHOD - I
Sin² C + Cos² C = 1
Cos² C = 1 - Sin² C
Cos² C = [tex]1 - \frac{9}{25}[/tex]
Cos² C = [tex]\frac{25 - 9}{25}[/tex]
Cos² C = [tex]\frac{16}{25}[/tex]
Cos C = [tex]\sqrt{\frac{16}{25} }[/tex]
Cos C = [tex]\frac{4}{5}[/tex]
As we know that
Tan C = [tex]\frac{Sin C}{Cos C }[/tex]
Tan C = [tex]\frac{\frac{3}{5} }{\frac{4}{5} }[/tex]
Tan C = [tex]\frac{3}{4}[/tex]
METHOD - II
Given Sin C = [tex]\frac{3}{5} = \frac{Height}{Hypotenuse}[/tex]
therefore,
AB ( Height ) = 3; BC ( Hypotenuse) = 5
∵ ΔABC is Right triangle.
∴ By Pythagorean Theorem-
AB² + AC² = BC²
AC² = BC² - AB²
AC² = 5² - 3²
AC² = 25 - 9
AC² = 16
AC ( Base) = 4
Since,
Tan C = [tex]\frac{Height}{Base}[/tex]
Tan C = [tex]\frac{AB}{AC}[/tex]
Hence Tan C = [tex]\frac{3}{4}[/tex]
