Question

If

θ

θ

is an acute angle of a right triangle and

tan θ=

3

5


tan⁡ θ=35

, what is the value of

cosθ

cos⁡θ

?

Answer 1

Given:

In a right angle triangle θ is an acute angle and
`\tan\theta =(3)/(5)`.

To find:

The value of
`\cos \theta`.

Solution:

In a right angle triangle,

`\tan \theta=(Perpendicular)/(Base)`

We have,

`\tan\theta =(3)/(5)`

It means the ratio of perpendicular to base is 3:5. Let 3x be the perpendicular and 5x be the base.

By using Pythagoras theorem,

`Hypotenuse=√(Perpendicular^2+base^2)`

`Hypotenuse=√((3x)^2+(5x)^2)`

`Hypotenuse=√(9x^2+25x^2)`

`Hypotenuse=√(34x^2)`

`Hypotenuse=x√(34)`

In a right angle triangle,

`\cos \theta=(Base)/(Hypotenuse)`

`\cos \theta=(5x)/(x√(34))`

`\cos \theta=(5)/(√(34))`

Therefore, the value of
`\cos \theta` is
`(5)/(√(34))`.