Mathematics: 25 POINTS!!PLEASE HELP Given tan(0)=5/6, then cos(0)=a/b. Determine the values of a and b

uhhn 980 oppsStep-by-step explanation:...

25 POINTS!!PLEASE HELP Given tan(0)=5/6, then cos(0)=a/b.

girlchamp654

12.02.2022

Value of a= 6

Value of b= 7.81

Step-by-step explanation:

We are given $tan \theta=\frac{5}{6}$

and $cos \theta=\frac{a}{b}$

We need to find values of a and b

We know that: $tan \theta=\frac{Perpendicular}{Base}$

While $cos \theta = \frac{Base}{Hypotenuse}$

So, a = Base and b= Hypotenuse

We know the value of base i,e $tan \theta=\frac{Perpendicular}{Base}=\frac{5}{6}$

We get Base=6, Perpendicular = 5

To find Hypotenuse we can use Pythagoras theorem

$(H)^2=(P)^2+(B)^2\\H^2=(5)^2+(6)^2\\H^2=25+36\\H^2=61\\H=\sqrt{61}\\H=7.81$

The value of hypotenuse is 7.81

The value of Base is 6

So, $cos \theta = \frac{Base}{Hypotenuse} =\frac{a}{b}= \frac{6}{7.81}$

Value of a= 6

Value of b= 7.81

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