Question

? Help if you know how to do this

Answer 1

`x = 2.5`

Explanation:

Given

`AC = 2x - 1`

`AB = 2x + 1`

`BC = 2\sqrt{7`

`\angle A = 60^(\circ)`

Required

Find x

To find x, we make use of cosine formula which states:

`a^2 = b^2 + c^2 - 2bcCosA`

In this case:

`BC^2 = AB^2 + AC^2 - 2*AB*BC*CosA`

Substitute values

`(2√(7))^2 = (2x + 1)^2 + (2x-1)^2 - 2*(2x + 1)*(2x - 1)*Cos(60^(\circ))`

Evaluate all exponents

`4*7 = (4x^2 + 4x + 1)+(4x^2 - 4x + 1) - 2(4x^2 - 1)*cos(60^(\circ))`

Open brackets

`28 = 4x^2 + 4x + 1+4x^2 - 4x + 1 - (8x^2 - 2)*cos(60^(\circ))`

Collect Like Terms

`28 = 4x^2 +4x^2+ 4x - 4x+ 1 + 1 - (8x^2 - 2)*cos(60^(\circ))`

`28 = 8x^2+ 2 - (8x^2 - 2)*cos(60^(\circ))`

Substitute 0.5 for cos(60)

`28 = 8x^2+ 2 - (8x^2 - 2)*0.5`

Open bracket

`28 = 8x^2+ 2 - 4x^2 + 1`

Collect Like Terms

`8x^2- 4x^2 + 2 + 1 - 28 = 0`

`4x^2 -25 = 0`

Collect Like Terms

`4x^2 =25`

Divide both sides by 4

`x^2 =(25)/(4)`

`x^2 =6.25`

Take positive square root of both sides

`x = \sqrt{6.25`

`x = 2.5`