The diagram shows triangle abc, with ab = xcm, ac = (x+2)cm, bc = 2square root7cm and angle cab = 60°.
(i) find the value of x.

4

Step-by-step explanation:

Angle CAB is opposite to the side BC.

We are going to use law of cosines to see this up since we are either given a numerical value or an algebraic expression per each side, and that we are also given an angle measurement for one of the 3 angles of our triangle.

Simplify and use foil to multiply/expand :

Using and doing a little simplifying gives:

Since 2(1/2)=1 we have:

Distribute:

Subtract 28 on both sides and simplify:

Find two numbers that multiply to be -24 and add to be 2.  Those numbers are 6 and -4 so the factored form of the right hand is given in the equation:

This implies x+6=0 or x-4=0.

Solving the first equation for x gives us x=-6 (subtracted 6 on both sides).

Solving the second equation for x gives us x=4 (added 4 on both sides).

4 is the only one that can be a solution since a side can't have a negative measurement.

The answer is x=4.

step-by-step explanation:

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