Calculate the side lengths a and b to two decimal places

A) a = 11.08 and b = 12.94

Step-by-step explanation:

We will use the law of sines to answer this problem.

First we find the measure of the missing angle.  The sum of the measures of the angles of a triangle is 180°.  The two given angles are 58 and 82; this gives us 58+82 = 140°.  This leaves the third angle as 180-140 = 40°.

The law of sines is

We have the measures of ∠C and side c; this makes the first ratio in our proportion

To find the measure of side a, our proportion will be

Cross multiplying, we have

a(sin 40) = 8.4(sin 58)

Divide both sides by (sin 40):

a(sin 40)/(sin 40) = 8.4(sin 58)/(sin 40)

a = 11.08

To find the length of side b, we use our original ratio

and the proportion

Cross multiplying,

b(sin 40) = 8.4(sin 82)

Divide both sides by (sin 40):

b(sin 40)/(sin 40) = 8.4(sin 82)/(sin 40)

b = 12.94

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: