Question

if cos theta =4/5 then find the value of tan theta is ________

Answer 1

Cos theta = 4/5 = B/H

B = 4 , H = 5 , P = ?

USING PATHAGOROUS THEOREM,

H² = P²+B²

P² = H² - B²

P² = (5)² - (4)²

P² = 25-16

P² = 9

P = ✓9 = 3

Therefore,

Tan theta = P/B= 3/4 .

HOPE IT WILL HELP YOU..

Answer 2

Given: cos theta = 4/5

To find: Value of tan theta

Solution: In a triangle, let base be denoted by b, perpendicular by p, hypotenuse by h and angle between hypotenuse and base be theta.

Then, cos theta

= base / height

= b/h

But cos theta = 4/5

Therefore, let

b = 4k and h = 5k

For finding p, we use Pythagoras' theorem:

${h}^{2} = {p}^{2} + {b}^{2}$

$= > {p}^{2} = {h}^{2} - {b}^{2}$

$= > {p}^{2} = {5k}^{2} - {4k}^{2}$

$= > {p}^{2} = (25 - 16) {k}^{2}$

$= > {p}^{2} = 9 {k}^{2}$

$= > p = 3k \: or \: - 3k$

But since length of side cannot be negative,

p = 3k

In the triangle, tan theta is

= perpendicular/base

= p/b

= 3k/4k

= 3/4

Therefore, the value of tan theta is 3/4.