Answer:
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
