Question

Please help with the question in the picture!

Answer 1

Tan C = 3/4

Explanation:

Given-

∠ A = 90°, sin C = 3 / 5

METHOD - I

Sin² C + Cos² C = 1

Cos² C = 1 - Sin² C

Cos² C =
`1 - (9)/(25)`

Cos² C =
`(25 - 9)/(25)`

Cos² C =
`(16)/(25)`

Cos C =
`\sqrt{(16)/(25) }`

Cos C =
`(4)/(5)`

As we know that

Tan C =
`(Sin C)/(Cos C )`

Tan C =
`((3)/(5) )/((4)/(5) )`

Tan C =
`(3)/(4)`

METHOD - II

Given Sin C =
`(3)/(5) = (Height)/(Hypotenuse)`

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 =
`(Height)/(Base)`

Tan C =
`(AB)/(AC)`

Hence Tan C =
`(3)/(4)`