Solve for x

Question

The perimeter of a triangle is 10 (that is, a+x+(x+1)=10).

Use this and the cosine law to solve for x. Round answers to 2 decimal places.

 

Triangle:

<BAC: 60degrees

 

line BA: x

line AC: X+1

line BC: a

Answer 1

If one of the angles in any triangle is 60 degrees, then you have an equilateral triangle.  This means that all the angles are the same and all the sides of the same.

 

The law of cosine equation would be easy to set up due to the type of triangle we have.

 

(BC)² = (BA)² + (AC)² - 2(BA)(AC)Cos(BAC)

 

Side BC is opposite to angle BAC.

 

 

Substituting in the variables,

 

a² = x² + (x + 1)² - 2x(x + 1)Cos(60)                  eq1    ---->  law of cosine

 

a + x + (x + 1) = 10                               eq2   ---> perimeter

 

 

Then simplifying both equation,

 

a² = x² + (x² + 2x + 1) - 2x(x + 1)(1/2)

 

a² = 2x² + 2x + 1 - x(x + 1)

 

a² = 2x² + 2x + 1 - x² - x

 

 

 

a² = x² + x + 1                         eq1

 

a + 2x = 9                                 eq2

 

 

Now use the substitution/elimination method to solve for x.