Use the Law of Sines to solve for all possible triangles tha

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does DNE. Round your answers to one decimal place. Below, enter your answers so that is smaller than) Find the indicated angle theta. (Use either the law of sines or the law of cosines, as appropriate. Assume a = 14, b = 4, and c = 15.)

Solution

b= 47 ; c = 42; C = 32 deg

using sine rule: c/sinC b/sinB

sinB = b*sinC/c = 47*sin32/42 = 0.593

Angel B1 = 36.4 deg ; Angle B2 = 180 -36.4 = 143.6 deg

AngleA1 = 180 -36.4 -32 = 111.6 \' Angle A2 = 180 -143.6 - 32 = 4.4 deg

a1/sinA1 = b/sinB1

a1 = sin111.6 *47/sin36.4 = 73.6

a2 = sinA2*b/sinB2 = sin4.4 *47/sin143.6 = 6.1