Cos and Tan

Question

In triangle RST, angle T is a right angle, RS=10 and ST=5

Find cos S and tan R to the nearest hundredth

Answer 1

You have a right triangle here

The Very First thing you should do is make a sketch!!

Then you will see that the adjacent side to S is 5 and that the hypotenuse is 10

 

Now you can find the cos(S) = adj/hyp = 5/10

 

The tangent is = sin/cos or = opp/adj

The opposite side from R is the adj side to S or ST = 5

 

You need to find the adjacent side to R

You need Pythagorean Theorem to do that.  hyp = RS

RS^2 = ST^2 + RT^2

10^2 =  5^2 + RT^2

RT^2 = 10^2 - 5^2 =

RT = √( 10^2 - 5^2 )

 

Now you can figure out the tan(R) = opp/adj = 5/RT

 

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