athXL mework Section 72 Ex Score 1 of 3 pts HW Score 3286 46

athXL mework: Section 7.2 Ex. Score: 1 of 3 pts HW Score: 32.86% (4.6 of 14 pts) F\'ind the unknown angles in triangle ABC, if the triangle exists. B-34.8 a 37.4 b 33.4 How many possible solutions does this triangle have? (Simplify your answer. Type an integer or a decimal) For the first solution, the angle A is 39.7o, the measure of angle C is 105.5. to Press Continue to see more 2 parts remaining

Solution

1) B = 34.8 deg ; a=37.4 ; b = 33.4

apply sine rule to find angleA

a/sinA = b/sinB

sinA = a*sinB/b = 37.4*sin34.8/33.4 = 0.639

A1 = 39.72 deg ; A2 = 180 -A1 = 140.278 deg

C1 = 180 - B-A1 = 105.48 ; C2 = 180 - 37.4 - 140.278 = 2.322 deg

So, two triangle are possible

2) C = 61deg41\' =61.68 deg ; c = 32.9 b = 26.9

apply sine rule:

b/sinB = c/SinC

sinB = b*sinC/c = 26.9*sin61.68/32.9 = 0.719

B1 = 46.035 deg ; B2 = 180 - B1 = 133.96 deg

A1 = 180 -B1 -C = 72.285 ; A2 = -15.64 (not possible)

So, only one triangle with Angle B = 46.035 = 46 deg