In the first one, use law of cosines.
In the triangle, you have two known sides, and one known angle of 48.5
The triangle should have the given angle is acts opposite to side A.
Alternatively you can use law of sines, twice to get the answer.
In this case, you will find angle B. sinB/314=sin(48.5)/527. once you simplify for sinB, use arcsin to find the angle. Then you can find angle C by summing up angle A and angle B, and subtracting from 180 (180degrees in a triangle). Then you can use law of sines again to find side C. This would look like sinB/314=sinC/C where sinB and sinC are known values.
In the second one, use the law of sines.
In the triangle, you have 2 known angles. an angle of 84.4, and an angle of 28.6. from there you can use law of sines.
You can find the third angle by summing up the two angles, and subtracting from 180. Lets call that angle C. We know side C. It is 107, the distance the tourist stands from the base.
sinC/C=sinB/B. where B is the unknown value, and sinC, C, and sin B are all known values.
This post was edited by thestoryofisaac on Jun 25 2014 11:55pm