Answer:
Value of a= 6
Value of b= 7.81
Step-by-step explanation:
We are given [tex]tan \theta=\frac{5}{6}[/tex]
and [tex]cos \theta=\frac{a}{b}[/tex]
We need to find values of a and b
We know that: [tex]tan \theta=\frac{Perpendicular}{Base}[/tex]
While [tex]cos \theta = \frac{Base}{Hypotenuse}[/tex]
So, a = Base and b= Hypotenuse
We know the value of base i,e [tex]tan \theta=\frac{Perpendicular}{Base}=\frac{5}{6}[/tex]
We get Base=6, Perpendicular = 5
To find Hypotenuse we can use Pythagoras theorem
[tex](H)^2=(P)^2+(B)^2\\H^2=(5)^2+(6)^2\\H^2=25+36\\H^2=61\\H=\sqrt{61}\\H=7.81[/tex]
The value of hypotenuse is 7.81
The value of Base is 6
So, [tex]cos \theta = \frac{Base}{Hypotenuse} =\frac{a}{b}= \frac{6}{7.81}[/tex]
Value of a= 6
Value of b= 7.81
