SOLUTION: Triangle ABC is inscribed in a semicircle of diameter a = 12 (a) If x denotes the length of side AC, express the length y of side BC as a function of x. (Hint: Angle ACB is a ri

Question 1145973: Triangle ABC is inscribed in a semicircle of diameter a = 12
(a) If x denotes the length of side AC, express the length y of side BC as a function of x. (Hint: Angle ACB is a right angle.)
(b) Express the area 𝒜 of triangle ABC as a function of x.
(c) State the domain of this function.
Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
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We have right angled triangle ABC with the right angle at vertex A.

 
The hypotenuse length is "a" units, and the leg AC has the length x (given).



(a)  Apply Pythagorean theorem :  | BC | =  = .


     it is the expression you are looking for.




(b)  Area is half of the product of leg lengths


        A = .



(c)  The domain of this function is  0 < x < 12.


      The endpoints 0 and 12 are not included to the domain, since otherwise the triangle becomes degenerated.

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