Answer:
57.0°, 123.0°
84.0°, 96.0°
56.9,
Step-by-step explanation:
Given:
a = 36, c = 48, ∠A = 39°
∠B1 is larger than ∠B2
Find attached the diagram.
We would apply sine rule to find ∠C
a/sinA = c/sinC
36/sin39° = 48/sinC
36sinC = 48sin39
sinC = 48sin39/36 = 48(0.6293)/36
sin C = 0.8391
C = arcsin(0.8391)
C= 57.045
∠C1 = C = 57.0° (1 decimal place)
For sine rule, angles which give same value are x and (180-x)
If C= x = 57.0°
180-x = 180 - 57.0° = 123°
∠C2 = 123.0°
sin57° = sin123° = 0.8387
∠A + ∠B + ∠C = 180° (sum of angles I'm a triangle)
39.0 + ∠B +57.0 = 180°
∠B = 180-(39+57)
∠B = 84.0°
∠B1 = 84.0°
∠B2 = 180-∠B1 = 180°-84.0°
∠B2 = 96.0°
∠B1 is smaller than ∠B2
b/sinB = c/sinC
b1/sinB1 = c1/sinC1
b/sin84 = 48/sin57
b = 48sin84/sin57
b = 56.9
The measure of C is 57.0 and the measure of B is 84.0 degrees
The given parameters are:
[tex]\mathbf{a = 36cm}[/tex]
[tex]\mathbf{c = 48cm}[/tex]
[tex]\mathbf{\angle A = 39^o}[/tex]
The measure of angle Ais calculated using the following sine formula
[tex]\mathbf{\frac{a}{sin\ A} = \frac{c}{sin\ C}}[/tex]
So, we have:
[tex]\mathbf{\frac{36}{sin\ 39} = \frac{48}{sin\ C}}[/tex]
Evaluate sin 39
[tex]\mathbf{\frac{36}{0.6293} = \frac{48}{sin\ C}}[/tex]
Cross multiply
[tex]\mathbf{sin\ C \times 36 = 48 \times 0.6293}[/tex]
[tex]\mathbf{sin\ C \times 36 = 30.2064}[/tex]
Divide both sides by 36
[tex]\mathbf{sin\ C= 0.8391}[/tex]
Take arc sin of both sides
[tex]\mathbf{C = sin^{-1}(0.8391)}[/tex]
[tex]\mathbf{C = 57.0}[/tex]
The value of B is:
[tex]\mathbf{B = 180 - A - C}[/tex]
So, we have:
[tex]\mathbf{B = 180 - 39 - 57.0\\}[/tex]
[tex]\mathbf{B = 84.0}[/tex]
Hence, the measure of C is 57.0 and the measure of B is 84.0 degrees
Read more about sine equations at:
https://brainly.com/question/14140350
