Trigonometric Question

[chilly saffron]

I used cosine rule, and I ended up here:

x^2 + 4x + 4 = 9x^2 + 60x + 100 + 49x^2 - 42x^2 + 140x * Cos(A)

Idk how to proceed from there

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[vagrant grotto]

I got x=3

By first cos60°

@chilly saffron

[chilly saffron]

how?

[torpid seal]

Show your work.

[chilly saffron]

@torpid seal

[torpid seal]

What's the law of cosines?

[chilly saffron]

a^2 = b^2 + c^2 - 2b * Cos(A)

@torpid seal

[torpid seal]

And which side is a?

[chilly saffron]

(x+2)

[torpid seal]

...in the general form, which side is a?

[chilly saffron]

wdum

[torpid seal]

...draw the triangle ABC that is used to illustrate the law of cosines.

[chilly saffron]

ok done

[torpid seal]

Show me.

[chilly saffron]

k wait lemme get my phone

[torpid seal]

...label the angles.

[torpid seal]

So which angle is A?

[chilly saffron]

In the question?

[torpid seal]

In the picture you just drew.

[chilly saffron]

The top side

[torpid seal]

But not always because we can rotate the triangle.

[chilly saffron]

Yeah

[torpid seal]

Describe it in a way that is always true.

[chilly saffron]

A is the missing angle?

[torpid seal]

But it's not missing. It's right there.

[chilly saffron]

A is the opposite angle of the side a?

[torpid seal]

Very good. So in the problem, what is the angle opposite the side with length x + 2?

[chilly saffron]

Theta

[torpid seal]

Not 60.

[chilly saffron]

Yeah

[torpid seal]

So do you see what you did wrong?

[chilly saffron]

No...

[torpid seal]

Look back here.

[chilly saffron]

I'm not supposed to find theta?

[torpid seal]

...does the question ask for theta?

[chilly saffron]

No

Asks us to make a quadratic formula

I could've used 60

And 3x+10 as A

[torpid seal]

Right. Because what you did ended up creating an equation with two variables.

[chilly saffron]

OK now I know how to answer it