Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form.
1 answer:
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Answer:
The vertex of this parabola, , can be found by completing the square.
Step-by-step explanation:
The goal is to express this parabola in its vertex form:
,
where ,
, and
are constants. Once these three constants were found, it can be concluded that the vertex of this parabola is at
.
The vertex form can be expanded to obtain:
.
Compare that expression with the given equation of this parabola. The constant term, the coefficient for , and the coefficient for
should all match accordingly. That is:
.
The first equation implies that is equal to
. Hence, replace the "
" in the second equation with
to eliminate
:
.
.
Similarly, replace the "" and the "
" in the third equation with
and
, respectively:
.
.
Therefore, would be equivalent to
. The vertex of this parabola would thus be:
.
We convert degrees to radian by multiplying by (
)
= (345) × ( )
= () × (π)
= 1.9166π
= 1.9166 × 3.14
= 6.018 rad
≈ 6.02 rad