Plz help (1 Viewer)

Sy123 · May 4, 2013

cricketfan1997 said:
View attachment 28076

Since the angle sum of a triangle is 180 degrees

$180^{\circ} = \angle BAC + \theta + 45^{\circ}$

$135^{\circ} - \theta = \angle BAC$

Using the sine rule:

$\frac{AC}{\frac{1}{\sqrt{2}}} = \frac{\sqrt{2}}{\sin(135^{\circ} - \theta)}$

Since this is Extension 1, we can expand the sine function

$AC = \frac{1}{\sin(135^{\circ}) \cos \theta - \sin \theta \cos(135^{\circ})}$

Now:

$\cos{135^{\circ}} = \cos(180 - 45)^{\circ} = -\cos 45^{\circ} = \frac{-1}{\sqrt{2}}$ Angle in second quadrant, cosine negative.

$\sin(180-45)^{\circ} = \sin 45^{\circ}$ Angle in second quadrant, sine positive.

Sub this back in:

$AC = \frac{1}{\cos \theta \frac{1}{\sqrt{2}} + \sin \theta \frac{1}{\sqrt{2}}}$

Multiply both top and bottom by the square root of 2.

$AC = \frac{\sqrt{2}}{\sin \theta + \cos \theta}} \ \ \ \square$

cricketfan1997 · May 4, 2013

Sy123 said:
Since the angle sum of a triangle is 180 degrees

$180^{\circ} = \angle BAC + \theta + 45^{\circ}$

$135^{\circ} - \theta = \angle BAC$

Using the sine rule:

$\frac{AC}{\frac{1}{\sqrt{2}}} = \frac{\sqrt{2}}{\sin(135^{\circ} - \theta)}$

Since this is Extension 1, we can expand the sine function

$AC = \frac{1}{\sin(135^{\circ}) \cos \theta - \sin \theta \cos(135^{\circ})}$

Now:

$\cos{135^{\circ}} = \cos(180 - 45)^{\circ} = -\cos 45^{\circ} = \frac{-1}{\sqrt{2}}$ Angle in second quadrant, cosine negative.

$\sin(180-45)^{\circ} = \sin 45^{\circ}$ Angle in second quadrant, sine positive.

Sub this back in:

$AC = \frac{1}{\cos \theta \frac{1}{\sqrt{2}} + \sin \theta \frac{1}{\sqrt{2}}}$

Multiply both top and bottom by the square root of 2.

$AC = \frac{\sqrt{2}}{\sin \theta + \cos \theta}} \ \ \ \square$

hey thanks man. if this wasn't extension one, what would you do other than expanding the trig function?

cricketfan1997 · May 5, 2013

Plz help (1 Viewer)

cricketfan1997

Member

Sy123

This too shall pass

cricketfan1997

Member

cricketfan1997

Member

Users Who Are Viewing This Thread (Users: 0, Guests: 1)