Answer:
58.25
Step-by-step explanation:
58 1/4 in decimal form = 58.25
True
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Find Angle B: B = 180 - (82+55) = 43. Then apply the law of sines:
b 8 cm
--------- = ----------
sin 43 sin 55
(sin 43)(8 cm)
Solving for b, we get b = ------------------- = 6.66, or 6.7 (cm, to the nearest tenth).
sin 55
Distance between points
![\left(x_1,y_1\right)](https://tex.z-dn.net/?f=%5Cleft%28x_1%2Cy_1%5Cright%29)
and
![\left( x_2,y_2 \right)](https://tex.z-dn.net/?f=%5Cleft%28%20x_2%2Cy_2%20%5Cright%29)
is
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2)
Distance from H to B:
![[tex]d=\sqrt{(10-(-3))^2+(1-(-9))^2}=\sqrt{169+100}=\sqrt{269}](https://tex.z-dn.net/?f=%5Btex%5Dd%3D%5Csqrt%7B%2810-%28-3%29%29%5E2%2B%281-%28-9%29%29%5E2%7D%3D%5Csqrt%7B169%2B100%7D%3D%5Csqrt%7B269%7D)
d=\sqrt{(1-(-3))^2+(10-(-9))^2}=\sqrt{16+361}=\sqrt{376}[/tex] units.
Distance from Z to B:
![d=\sqrt{(10-(-3))^2+(1-(-9))^2}=\sqrt{169+100}=\sqrt{269}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%2810-%28-3%29%29%5E2%2B%281-%28-9%29%29%5E2%7D%3D%5Csqrt%7B169%2B100%7D%3D%5Csqrt%7B269%7D)
units.
Horse Z is closer to the barn.
(The conversion to meters is not required; the question does not ask for actual distances, so "units" is OK.)
hard to tell but from 0.75 to 1