Question

In a right triangle, 0 is an acute angle and tan 0=8/5. What is the exact value of cos 0?

Answer 1

`\cos\theta=0.53`

Explanation:

Given that,

`\tan\theta=(8)/(5)`

We know that,

`\tan\theta=(P)/(B)`

Where

P is perpendicular and B is base

Let H is hypotenuse of triangle. Using Pythagoras theorem,

`H^2=P^2+B^2\\\\H=√(P^2+B^2) \\\\H=√(8^2+5^2) \\\\H=9.43`

We know that,

`\cos\theta=(B)/(H)\\\\\cos\theta=(5)/(9.43)\\\\\cos\theta=0.53`

So, the value of
`\cos\theta` is equal to 0.53.