Question

Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.

Answer 1

Answer:

A=98.05°, B= 40°,  C= 41.95, a=38.5, b = 25, c = 26 ....

Step-by-step explanation:

According to the law of sine:

a / sin(A) = b / sin(B) = c / sin(C)

or you can also write it as:

sin(A) / a = sin(B) / b = sin(C) / c  

We have:

B = 40°, b = 25, c = 26

We will use sin(B) / b = sin(C) / c to find angle C

sin(B) / b = sin(C) / c

Substitute the values in the rule:

sin(40)/25 = sin(C)/26

Multiply both sides by 26.

26*sin(40)/25 = sin(C)

26* 0.642788/25 = sin(C)

16.712488/25= sin(C)

0.66849952= sin(C)

sin−1(0.66849952)= C

41.95 degrees = C

Now we know that A+B+C=180°

Therefore put the values in the equation:

A+40+41.95=180°

A+81.95=180°

A=180°-81.95°

A=98.05°

Now take first two elements of sine rule:

a / sin(A) = b / sin(B)

a/sin(98.05°)= 25/sin(40°)

a=25*sin(98.05°)/sin(40°)

a=25(0.9901)/0.64278

a=24.7525/0.64278

a= 38.5

There fore

A=98.05°, B= 40°,  C= 41.95, a=38.5, b = 25, c = 26 ....

Answer 2

Answer:Explained

Step-by-step explanation:

Given

$B=40^{\circ}$

b=25

c=26

Using sine rule

$\frac{b}{sinB}=\frac{c}{sinC}$

$sinC=sinB\frac{c}{b}$

$sinC=sin40\cdot \frac{26}{25}$

C=41.94 and corresponding A=98.06

$\pi -C=41.94$

C=138.06 and A=1.94