Question

Find the value of tan x if 5sin x=3​

Answer 1

★Given:-

• 5sin x = 3

★To find:-

• Value of tan x

★Solution:-

Given,

→5sin x = 3

⇒sin x = 3/5

We know,

✦Sin x = opposite side/hypotenuse

Hence,

→Opposite side = 3

→Hypotenuse = 5

Using pythagoras theorem,

✦(Opposite side)²+(Adjacent side)²=(Hypotenuse)²

Putting values,

⇒ 3² + (Adj)² = 5²

⇒ (Adj)²= 5²-3²

⇒ (Adj)² = 25 - 9

⇒ Adj = √16

⇒ Adjacent side = 4cm

Using the formula,

✦Tan x = Opposite side/Adjacent side

Putting values,

→Tan x = 3/4

Hence, the values of tan x is 3/4

______________

Know more:-

More formula's:

• Tan x = sin x/cos x

• Sin x = 1/cosec x

• Cosec x = Hypotenuse / opposite side

• Tan x = 1/cot x

• Cot x = Adjacent side/opposite side

______________

Answer 2

Given :-

$\sf{★\ 5 \ sin \ x = 3}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

To find :-

$\sf{★ \ value \ of \ tan \ x}$

Solution :-⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

5 Sinx = 3

Sinx = 3 / 5

• We know that ,

SinΦ = Perpendicular / Hypotenuse.

Hypotenuse² = Perpendicular² + Base²

5² = 3² + Base²

25 - 9 = Base²

16 = Base²

$\sf\pink{⟹ \ Base \ = \ 4}$

• Tanx = Perpendicular / Base

Tan x = 3 / 4

$\large{\boxed{\boxed{\sf{★ \ Tan x = 3 / 4 }}}}$