HELP

A) 7.8
C) 6.2
B) 8.5
D) 11.6​

Step-by-step explanation:

this is tuff.  but we can solve for x where  x is the short distance along the smaller triangle.  Not that long distance along both triangles,  so,  we can find all the angles by using that the interior angles of a triangle add to 180°

bigger triangle :   180 =  90 + 66 + w       subtract 90+60 from 180 so  w= 23

smaller triangle:  180 = 48+90+V  subtract 48+90 from 180  so V =42

since we are told that the Hypotenuse of the big triangle is 23 units, then we can solve for what the length of the side that both triangles share by using

SOH CAH TOA to recall how the trig functions fit on a triangle

SOH: Sin(Ф)= Opp / Hyp

CAH: Cos(Ф)= Adj / Hyp

TOA: Tan(Ф) = Opp / Adj

then pick which one has the two knows and the unknown we want to find

we have the angle and they Hyp and  want to find the Opposite side, so let's use  Sin

Sin(23) = Opp / 23

23*Sin(23) = Opp

8.9868 = Opp

Now we know 2 angles and one side of the smaller triangle

so use the law so Sines to find that other side which is  x

law of Sines Sin(A) /a = Sin(B) / b

we can let b = x

Sin(48) / 8.9868 = Sin(42) / x

we need to do some algebra here to solve for x,  i'll do the algebra in letters then plug in what we have above

A / B = C / x

x / C = B / A

x = C ( B / A )

now plug in knowns

x = Sin(42) * ( 8.9868 / Sin( 48 ))

x = 8.0917

the more rounding error we get the closer it gets to 7.8 so while that one is off, that seems to be the closest one.. unless there are other answers closer to the X I've found above  try 7.8

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