The angles in triangle are in the ratio of 2:2:4. Find the exterior angle adjacent to the largest angle.
1 answer:
The sum of all interior angles in a triangle is 180°.
the angles in this triangle are on a 2:2:4, we know if we add all those three angles, we'd end up with 180°, therefore then 180 is on a 2:2:4 ratio.
in other words, 180 divided by (2+2+4) gives us 22.5°.
now, we know one angle takes 2 of those 22.5, so is 22.5+22.5 or 45°.
the other angle takes the same 2 of those, so is also 45°.
and the largest one takes 4 of those, so is 22.5(4) or 90°.
now, what's the exterior angle to a 90° angle? check the picture below.
the angles in this triangle are on a 2:2:4, we know if we add all those three angles, we'd end up with 180°, therefore then 180 is on a 2:2:4 ratio.
in other words, 180 divided by (2+2+4) gives us 22.5°.
now, we know one angle takes 2 of those 22.5, so is 22.5+22.5 or 45°.
the other angle takes the same 2 of those, so is also 45°.
and the largest one takes 4 of those, so is 22.5(4) or 90°.
now, what's the exterior angle to a 90° angle? check the picture below.
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All we need is to put this form in the vertex form f(x) = (ax+b)^2 + c
So we have <span>f (x)= 3x^2+12x+11 ....
Let's complete the square (if you aware of it)
</span><span>
f(x)= 3x^2+12x+11 = 3(x^2+4x)+11 = 3(x^2+4x+4-4)+11
=</span><span> 3([x^2+4x+4]-4)+11 = 3[(x+2)^2-4]+11 =3</span><span>(x+2)^2 - 12 +11 = 3</span><span><span>(x+2)^2 -1
so our form would be:
Here is a parabola with vertex of (-2,-1) and with positive </span> slope (concave up)
</span>
So we have <span>f (x)= 3x^2+12x+11 ....
Let's complete the square (if you aware of it)
</span><span>
f(x)= 3x^2+12x+11 = 3(x^2+4x)+11 = 3(x^2+4x+4-4)+11
=</span><span> 3([x^2+4x+4]-4)+11 = 3[(x+2)^2-4]+11 =3</span><span>(x+2)^2 - 12 +11 = 3</span><span><span>(x+2)^2 -1
so our form would be:
Here is a parabola with vertex of (-2,-1) and with positive </span> slope (concave up)
</span>
I hope that helps!