Find tan(2 Theta +pi) using the picture:

Question

You have a right triangle and the hypotenuse is 10 and adjacent side is 6 and the opposite side is 8,

this is what the triangle looks like except NO cm!

 

http://www.cimt.plymouth.ac.uk/projects/mepres/book9/bk9i15/s2q10.png

 

I am not sure how to solve this can someone help me please!!

 

 

  

Answer 1

My guess is the intent of this problem was to use trig identities for tan (x+y) and tan 2x.

 

tan(2x+pi) = (tan2x + tan pi)/(1-tan2xtanpi), Since tan pi = 0 we have this reducing to tan2x.

 

But tan2x = 2tanx/(1-tan²x). But from the diagram we know tanx = 3/4 (using x instead of theta),

 

Substituting 3/4 for x in last, gives 2(3/4)/(1 - (3/4)²) = 3/2 / 7/16 or 24/7.

Answer 2

 

Assuming that you are looking for the angle measure (theta) ... θ,

 

    Since you have all sides of the triangle ... 6, 8, and 10,

 

Determine whether this i a right triangle using Pythagorean theorem ... c² = a² + b²

    

    10² = 8² + 6²

    100 = 64 + 36

    100 = 100

 

This is a right triangle ... so we can use the trig ratios to find θ.

     For this triangle (in relation to θ),

          the adjacent side is 8

          the opposite side is 6

          the hypotenuse is 10 

 

     sine θ = opposite ÷ hypotenuse

 

     sine θ = 6/10

               = .6

 

Then use the inverse sin trig function (also called arcsin) on the calculator (sin^-1 .6) ... in degree mode, to find  θ in degrees

 

   θ = 64.35 degrees

 

Now that you have the value of theta, you can convert pi into degrees (180 degrees) and evaluate.

 

   tan (2 θ + pi)

= tan (2•64.35+ 180)

= -1.2482