The law of cosines is used to find the measure of Angle Q. Triangle Q R S is shown. The length of Q R is 20, the length of R S is 24, and the length of Q S is 34. To the nearest whole degree, what is the measure of Angle Q? 44º 49º 54º 59º

44º

Step-by-step explanation:

We are given that a triangle QRS

QR=20 units

RS=24 units

QS=34 units

We have to find the measure of angle Q.

We know that cosine law

Using the formula

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

answer:   14

step-by-step explanation:          

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