Solve triangle ABC If an answer does not exist enter DNE Rou

Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) To find the distance across a small lake, a surveyor has taken the measurements shown. Find the distance across shoreline, and that a = 2.92 miles and b = 3.81 miles. Round your answer to two decimal places.)

Solution

a = 25; b = 49 ; c =27

Applying cosine rule : a^2 = b^2 +c^2 -2bccosA

25^2 = 49^2 +27^2 - 2*49*27cosA

cos A= 0.946

AngleA = 18.9 deg

Now applying sine rule: b/sinB = a/sinA

sinB = b*sinA/a =0.634

Angle B1 = 39.4 deg ;

Angle B2 = 140.6

Angle C1 = 180 -A- B = 121.7 deg ;

Angle C2 = 180 - 18.9 - 140.6 = 20.5 deg