Question

Find tan theta where theta is the angle shown.

Answer 1

Here we would like to find out the value of given trigonometric ratio . A right angled triangle is given to us with perpendicular= 8 and hypotenuse= 11 . Firstly let's calculate the base using Pythagoras theorem as ,

`\longrightarrow h^2=p^2+b^2\\`

`\longrightarrow 11^2 = 8^2+b^2\\`

`\longrightarrow 121 = 64 + b^2\\`

`\longrightarrow b^2=121-64=57\\`

`\longrightarrow b =√(57)=7.54 \\`

Now we know that,

`\longrightarrow \tan\theta =(p)/(b)\\`

so substitute the respective values,

`\longrightarrow \tan\theta =(8)/(7.54)\\`

`\longrightarrow\underline{\underline{ \tan\theta = 1.06 \approx \boxed{1}}}`

and we are done!