Question

if sin tetta=5/8, find the value of tan tetta​

Answer 1

Answer:

Given that

sin(theta)=5/8

To find tan(theta)

by using

$cos(\theta)=\sqrt{1-sin^2(\theta)}\\cos(\theta)=\sqrt{1-\frac{25}{64}}=\frac{\sqrt{39} }{8}$

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}\\tan(\theta)=\frac{5/8}{\sqrt{39} /8}\\tan(\theta)=\frac{5}{\sqrt{39} }$

Step-by-step explanation:

Answer 2

Answer:

$\frac{5}{ \sqrt{39} }$

Step-by-step explanation:

Given:

sinѲ = ⅝

To Find:

Value of tanѲ

Formulas Used:

Pythagoras Theorem

sinѲ = perpendicular/hypotenuse

tanѲ = perpendicular/base

Assumption:

Since, sinѲ = ⅝(By formula)

Let the perpendicular be 5x and base be 8x

Solution:

According to Pythagoras theorem:

(hypotenuse)² = (perpendicular)² + (base)²

=> (8x)² = (5x)² + (base)²

=> 64x² = 25x² + (base)

=> 64x² - 25x² = (base)²

=> 39x² = (base)²

=> base = √39x²

=> base = √39x

tanѲ = perpendicular/base = 5x/√39x = 5/√39

Hope it helps you......✔✔✔