Question

Determine the number of possible triangles, ABC, that can be formed given B = 45°, b = 4, and c = 5.

Answer 1

Given:
m∠B = 45°
b = 4
c = 5

From the Law of Sines, obtain
$\frac{sinC}{c}= \frac{sinB}{b} \\ sinC=( \frac{c}{b})sinB \\sinC = ( \frac{5}{4} )sin(45^{o})=0.884\\ C = sin^{-1}0.884=62.1^{o}$
This yields
m∠A = 180 - 45 - 62.1 = 72.9°
$a=( \frac{sinA}{sinB})b=( \frac{sin(72.9^{o})}{sin(42^{o})})4=5.41$
The first triangle has
∠A=72.9°,  m∠B=45°,  m∠C = 62.1°,  a=5.41,  b=4,  c=5.

Also, 
$m\angle{C} = sin^{-1}0.884 = 117.9^{o}$
This yields
m∠A = 180 - 45 - 117.9 = 17.1°
$a=( \frac{sinA}{sin(45^{o})} )4=1.66$
The second triangle has
m∠A = 17.1°,  m∠B = 45°,  m∠C = 117.9°,  a = 1.66,  b = 4,  c = 5

Answer: There are 2 possible triangles.

Answer 2

Answer:

2

Step-by-step explanation:

this is right trust