Use the equivalents ...
... 1/3 = 2/6
... 9/18 = 3/6
... 1 = 6/6
First we split the mixed numbers into integer parts and fractional parts, adding each separately.
(5 1/3) + (-3 9/18) = (5 +(-3)) +(1/3 +(-9/18))
... = 2 + (2/6 - 3/6) . . . . . . use the equivalents for 1/3 and 9/18 to have a common denominator (6)
... = 2 - 1/6 . . . . . . . . . . . . the sum of the fractional parts is negative
... = (1 + 1) - 1/6 . . . . . . . . here's how we subtract it from the integer part
... = 1 + (6/6 - 1/6)
... = 1 5/6
You can use the Law of Sines for this problem, but what makes it tough at first glance is that they put a step in before you can use it directly. That first step is to get m∠C. When solving a triangle, always get the third angle if you know the other two so that you can use the Law of Sines (or Law of Cosines) more directly.
The sum of the angles of any triangles is 180°. We know the measures of the two other angles. So we subtract them from 180° to find that third angle.
180° - 76° - 66° = 38°
Now we can use the proportion from the picture. Angle B measures 76°, side b is our unknown, Angle C measures 38°, and side c measures 3 units.
sin 76° sin 38°
----------- = -----------
b 3
Cross multiply to find b (the side). We carry out five places in these calculations to get more accuracy.
3 * sin 76° = b * sin 38°
b = 3 * sin 76° 3 * 0.56611 1.69832
--------------- = --------------- = ---------------- = 5.73044
sin 38° 0.29636 0.29636
To the nearest tenth, b - 5.7 units.
