SOLUTION: What is cos Ø if tan Ø = 4/? A. 3/5 B. 3/4 C. 4/5 D. 5/4 E. 5/3 *show work*

Algebra ->  Proportions -> SOLUTION: What is cos Ø if tan Ø = 4/? A. 3/5 B. 3/4 C. 4/5 D. 5/4 E. 5/3 *show work*      Log On


   

Question 847408: What is cos Ø if tan Ø = 4/? A. 3/5 B. 3/4 C. 4/5 D. 5/4 E. 5/3 *show work*
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If that question mark is supposed to be 3, then

tan(theta) = 4/3

tan(theta) = opp/adj

so opp = 4, adj = 3

The two legs of this triangle are 4 and 3.

The hypotenuse is sqrt(4^2 + 3^2) = sqrt(25) = 5. You effectively use the Pythagorean Theorem to find the hypotenuse.

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cos(theta) = adj/hyp

cos(theta) = 3/5

Special note: this answer of 3/5 is only true IF tan(theta) = 4/3 (ie if my initial assumption above holds up)